EQUATION OF A CIRCLE
(1). Find the equation of the circle with center (3, -2) and radius 2 units
(A) x2+y2+6x+4y+9=0 (B) x2-y2-6x+4y+9=0 (C)x2+y2-6x+4y+9=0 (D)x2+y2-6x-4y-9=0
Solution:-Using CASIO fx-991MS calculator
From the centre (3, -2) make x=3, y=-2, let m=radius
When tracing the options put +m2 after the constant e.g. x2+y2+ax+by+c+m2=0. Since x = 3, y = -2, m = radius :.m = 2 units
Checking option A,B,C,D if it give zero it is correct but if it did not give zero it is wrong
Using CASIO fx-991MS calculator
[ON] [3] [SHIFT] [STO] [X] (x=3)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [(-)] [2] [SHIFT ] [STO] [Y] (Y=-2)
[AC] [2] [SHIFT] [STO] [M] (M=2)
Checking option(A) x2+y2+6x+4y+9=0
Don’t forget to put +m2 in all the objective options after the constant
Using CASIO fx-991MS calculator
[AC] [ALPHA] [X] [x2] [+] [ALPHA] [Y] [x2] [+] [6] [ALPHA] [X] [+] [4] [ALPHA] [Y] [+] [9] [+] [ALPHA] [M] [x2] [=](36)
Option A is wrong, check the next option
Checking Option (B) x2-y2-6x+4y+9=0
Don’t forget to put +m2 in all the objective options after the constant
[AC] [ALPHA] [X] [x2] [-] [ALPHA] [Y] [x2] [-] [6] [ALPHA] [X] [+] [4] [ALPHA] [Y] [+] [9] [+] [ALPHA] [M] [x2] [=](-8)
Option (B) is wrong go to the next option
Checking Option (C)x2+y2-6x+4y+9=0
Don’t forget to put +m2 in all the objective options after the constan
[AC] [ALPHA] [X] [x2] [+] [ALPHA] [Y] [x2] [-] [6] [ALPHA] [X] [+] [4] [ALPHA] [Y] [+] [9] [+] [ALPHA] [M] [x2] [=](0)
Option (C) is correct
Checking Option (D)x2+y2-6x-4y-9=0
Don’t forget to put +m2 in all the objective options after the constant
[AC] [ALPHA] [X] [x2] [+] [ALPHA] [Y] [x2] [-] [6] [ALPHA] [X] [-] [4] [ALPHA] [Y] [-] [9] [+] [ALPHA] [M] [x2] [=](-2)
Option D is wrong The correct option is option “C” you can use a porpo YH-2000calculcator for this kind
(2). Find the centre and the radius of the circle whose equation is x 2+ y2 – 10x + 8y – 59 = 0
(A) (-4, 5), 10 (B) (-5, 4), 10 (C) (-5, -4), 10 (D) (5, -4), 10
Solution:-Using CASIO fx-991MS calculator
Make x and y=any of the option given and m=any of the option given i.e. A, B, C, D to trace the answer add +m2 where m = radius i.e. x2 + y2 – 10x + 8y – 59 + m2 = 0
Checking option (A) (-4, 5), 10
[ON] [(-)] [4] [SHIFT] [STO] [X] (X=-4)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [5] [SHIFT ] [STO] [Y] (Y=5)
[AC] [1] [0] [SHIFT] [STO] [M] (M=10)
Typing the equation x2+y2-10x+8y-59+m2=0 using CASIO fx-991MS calculator
[AC] [ALPHA] [X] [x2] [+] [ALPHA] [Y] [x2] [-] [1] [0] [ALPHA] [X] [+] [8] [ALPHA] [Y] [-] [5] [9] [+] [ALPHA] [M] [x2] [=] (162)
Option A is wrong because is not equal to zero. Check the next option
Checking Option (B) (-5, 4), 10
[AC] [(-)] [5] [SHIFT] [STO] [X] (X=-5)
[AC] [4] [SHIFT ] [STO] [Y] (Y=4)
[AC] [1] [0] [SHIFT] [STO] [M] (M=10)
Press [↑] [↑] [↑] [=] (164)
Option B is wrong because is not equal to zero. Check the next option
Checking Option (C) (-5, -4), 10
[AC] [(-)] [5] [SHIFT] [STO] [X] (X=-5)
[AC] [(-)] [4] [SHIFT ] [STO] [X] (Y=-4)
[AC] [1] [0] [SHIFT] [STO] [M] (M=10)
Press [↑] [↑] [↑] [=] (100)
Option “C” is wrong because is not equal to zero. Check the next option
Checking Option (D) (5, -4), 10
[AC] [(-)] [5] [SHIFT] [STO] [X] (X=5)
[AC] [(-)] [4] [SHIFT ] [STO] [X] (Y=-4)
[AC] [1] [0] [SHIFT] [STO] [M] (M=10)
Press [↑] [↑] [↑] [=] (0)
The correct option is “D”
(3). Find the equation of circle passing through the points (3, 1), (-2, 6), (-5,-3)
(A) (x + 2)2 + (y + 1)2 = 25 (B) (x – 2)2 + (y + 1)2 = 25 (C) (x – 2)2 + (y – 1)2 = 25 (D) (x + 2)2 + (y – 1)2 = 25
Solution:-Using CASIO fx-991MS calculator. Make x and y = points given i.e. “(3, 1), (-2, 6), (-5,-3)
First point (3,-1) :. X = 3 y = -1
First point (3,-1) :. X = 3 y = -1
[ON] [3] [SHIFT] [STO] [X] (x=3)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [1] [SHIFT] [STO] [Y] (Y=-1)
[AC] [1] [SHIFT] [STO] [Y] (Y=-1)
Checking option (A) (x + 2)2 + (y + 1)2 = 25
If any of the options gives 25 it is correct but if it did not give 25 it is wrong
[AC] [(] [ALPHA] [X] [+] [2] [x2] [+] [(] [ALPHA] [Y] [+] [1] [)] [x2] [=] (41)
Option (A) is wrong because it did not give 25
Checking option (B) (x – 2)2 + (y + 1)2 = 25
If any of the options gives 25 it is correct but if it did not give 25 it is wrong
[AC] [(] [ALPHA] [X] [-] [2] [x2] [+] [(] [ALPHA] [Y] [+] [1] [)] [x2] [=] (9)
Option (B) is wrong because it did not give 25
Checking option (C) (x – 2)2 + (y – 1)2 = 25
If any of the options gives 25 it is correct but if it did not give 25 it is wrong
[AC] [(] [ALPHA] [X] [-] [2] [x2] [+] [(] [ALPHA] [Y] [-] [1] [)] [x2] [=] (41)
Option (C) is wrong because it did not give 25
Checking option (D) (x + 2)2 + (y – 1)2 = 25
If any of the options gives 25 it is correct but if it did not give 25 it is wrong
[AC] [(] [ALPHA] [X] [+] [2] [x2] [+] [(] [ALPHA] [Y] [-] [1] [)] [x2] [=] (25)
Option (D) is correct because it give 25. Since the first point gives 25
Impute the other points (-2, 6) make x = - 2, y = 6
[AC] [(-)] [2] [SHIFT] [STO] [X] (X=-2)
[AC] [6] [SHIFT ] [STO] [Y] (Y=6)
Press [↑] [↑] [=] (25)
Since the second point gives 25 Impute the other points(-5, -3) make x = - 5, y = - 3
[AC] [(-)] [5] [SHIFT] [STO] [X] (X=-5)
[AC] [(-)] [3] [SHIFT ] [STO] [Y] (Y=-3)
Press [↑] [↑] [=] (25)
The correct Option is “D”
Option (B) is wrong because it did not give 25
Checking option (C) (x – 2)2 + (y – 1)2 = 25
If any of the options gives 25 it is correct but if it did not give 25 it is wrong
[AC] [(] [ALPHA] [X] [-] [2] [x2] [+] [(] [ALPHA] [Y] [-] [1] [)] [x2] [=] (41)
Option (C) is wrong because it did not give 25
Checking option (D) (x + 2)2 + (y – 1)2 = 25
If any of the options gives 25 it is correct but if it did not give 25 it is wrong
[AC] [(] [ALPHA] [X] [+] [2] [x2] [+] [(] [ALPHA] [Y] [-] [1] [)] [x2] [=] (25)
Option (D) is correct because it give 25. Since the first point gives 25
Impute the other points (-2, 6) make x = - 2, y = 6
[AC] [(-)] [2] [SHIFT] [STO] [X] (X=-2)
[AC] [6] [SHIFT ] [STO] [Y] (Y=6)
Press [↑] [↑] [=] (25)
Since the second point gives 25 Impute the other points(-5, -3) make x = - 5, y = - 3
[AC] [(-)] [5] [SHIFT] [STO] [X] (X=-5)
[AC] [(-)] [3] [SHIFT ] [STO] [Y] (Y=-3)
Press [↑] [↑] [=] (25)
The correct Option is “D”
(4). Find the equation of the circle with centre at (5, -7) and passing through the point (2, -3)
(A)x2 + y2 + 10x – 14y + 49 = 0 (B) x2 + y2 – 10x + 14y + 49 = 0 (C) x2 + y2 – 10x + 14y – 49 = 0 (D) x2 + y2 – 10x + 14y + 49 = 0
Solution:-Using CASIO fx-991MS calculator
Since the radius m is not given to the bottom to use, don’t bother to use the centre given. Just use the points given to trace the answers e.g. point (2,-3) make x = 2 y = -3
[ON] [2] [SHIFT] [STO] [X] (X=2)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [(-)] [3] [SHIFT] [STO] [Y] (Y=-3)
Tracing the right options, if any of the options gives zero it is correct but if it did not give zero it is wrong
Checking option (A) x2 + y2 + 10x – 14y + 49 = 0
[AC] [ALPHA] [X] [x2] [+] [ALPHA] [Y] [x2] [+] [ALPHA] [Y] [x2] [+] [1] [0] [ALPHA] [X] [-] [1] [4] [ALPHA] [Y] [+] [4] [9] [=] (124)
Option (A) is wrong because it did not give zero
Checking option (B) x2 + y2 – 10x + 14y + 49 = 0
[AC] [ALPHA] [X] [x2] [+] [ALPHA] [Y] [x2] [-] [1] [0] [ALPHA] [X] [+] [1] [4] [ALPHA] [Y] [+] [4] [9] [=] (0)
Option (B) is correct because it give zero
Checking option (C) x2 + y2 – 10x + 14y – 49 = 0
[AC] [ALPHA] [X] [x2] [+] [ALPHA] [Y] [x2] [-] [1] [0] [ALPHA] [X] [+] [1] [4] [ALPHA] [Y] [-] [4] [9] [=] (-98)
Option (C) is wrong because it did not give zero
Checking option (D) x2 + y2 – 10x + 14y – 49 = 0
[AC] [ALPHA] [X] [x2] [+] [ALPHA] [Y] [x2] [-] [1] [0] [ALPHA] [X] [+] [1] [4] [ALPHA] [Y] [-] [4] [9] [=] (-98)
Option (C) is wrong because it did not give zero
Checking option (D) x2 + 2y2 – 10x + 14y + 49 = 0
[AC] [ALPHA] [X] [x2] [+] [2] [ALPHA] [Y] [x2] [-] [1] [0] [ALPHA] [X] [+] [1] [4] [ALPHA] [Y] [-] [4] [9] [=] (-89)
Option (D) is wrong because it did not give zero
(5). Which of the following points is on the circle x2 + y2 – 2x – 4y = 0
(A) (2, 4) (B) (7, 1) (C) (-4, 3) (D) (5, 0)
Solution:-Using CASIO fx-991MS calculator
Make x and y = any options given
Checking option (A) (2, 4) make x = 2, y = 4
[ON] [2] [SHIFT] [STO] [X] (X=2)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [4] [SHIFT] [STO] [Y] (Y=4)
Tracing the right options, if any of the options gives zero it is correct but if it did not give zero it is wrong
[AC] [ALPHA] [X] [x2] [+] [ALPHA] [ALPHA] [Y] [x2] [-] [2] [ALPHA] [X] [-] [4] [ALPHA] [Y[ [=] (0)
Option (A) is correct
Checking option (B) 7, 1 make x = 7, y = 1
[AC] [7] [SHIFT] [STO] [X] (X=7)
[AC] [1] [SHIFT ] [STO] [Y] (Y=1)
Press [↑] [↑] [=] (32)
Option (B) is wrong
Checking option (C) -4, 3 make x=-4, y=3
[AC] [(-)] [4] [SHIFT] [STO] [X] (X=-4)
[AC] [3] [SHIFT ] [STO] [Y] (Y=3)
Press [↑] [↑] [=] (21)
Option (C) is wrong
Checking option (D) (5, 0) make x = 5 y = 0
[AC] [5] [SHIFT] [STO] [X] (X=5)
[AC] [0] [SHIFT ] [STO] [Y] (Y=0)
Press [↑] [↑] [=] (15)
Option (D) is wrong
(6). Find the equation of the ellipse with vertices at (-6, 0) (6, 0) and foci at (-4, 0) (4, 0)
(A) X2 + y2 = 1 (B) x2 + y2 = 1 (C) x2 + y2 = 1 (D) x2 + y2 = 1
20 36 36 20 16 9 25 9
Solution:-Using CASIO fx-991MS calculator
Firstly use the vertices given to trace the options ±(6,0) = (-6,0) or (6,0)
You can take any one of the vertices, make x = ±6 or (x = 6, y = 0) any
Use it to trace option A, B, C, D
Checking option (A) X2 + y2 = 1
20 36
[ON] [6] [SHIFT] [STO] [X] (X=6)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [0] [SHIFT ] [STO] [Y] (Y=0)
[AC] [ALPHA] [X] [x2] [ab/c] [2] [0] [+] [ALPHA] [Y] [x2] [ab/c] [3] [6] [=] (14/5)
Option (A) is wrong go to the next option
Checking option (B) X2 + y2 = 1
36 20
[AC] [ALPHA] [X] [x2] [ab/c] [3] [6] [+] [ALPHA] [Y] [x2] [ab/c] [2] [0] [=] (1)
Option (B) is correct
Checking option (C) X2 + y2 = 1
16 9
[AC] [ALPHA] [X] [x2] [ab/c] [1] [6] [+] [ALPHA] [Y] [x2] [ab/c] [9] [=] (21/4)
Option (C) is wrong go to the next option
Checking option (D) X2 + y2 = 1
25 9
[AC] [ALPHA] [X] [x2] [ab/c] [2] [5] [+] [ALPHA] [Y] [x2] [ab /c] [9] [=] (111/25)
Option (D) is wrong
The correct option is (B) to find the foci use option (B) since option (B) is correct to get the foci use c2 = ±√A2 – B2 where A2 = 36 B2 = 20 since using the formula
X2 + y2 = 1
A2 – B2
Calculating c2 = ±√36 – 20 using the denominator, c2 = ±√16 c = ±4 = foci = (4,0), (-4,0)
(A) X2 + y2 = 1 (B) x2 + y2 = 1 (C) x2 + y2 = 1 (D) x2 + y2 = 1
20 36 36 20 16 9 25 9
Solution:-Using CASIO fx-991MS calculator
Firstly use the vertices given to trace the options ±(6,0) = (-6,0) or (6,0)
You can take any one of the vertices, make x = ±6 or (x = 6, y = 0) any
Use it to trace option A, B, C, D
Checking option (A) X2 + y2 = 1
20 36
[ON] [6] [SHIFT] [STO] [X] (X=6)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [0] [SHIFT ] [STO] [Y] (Y=0)
[AC] [ALPHA] [X] [x2] [ab/c] [2] [0] [+] [ALPHA] [Y] [x2] [ab/c] [3] [6] [=] (14/5)
Option (A) is wrong go to the next option
Checking option (B) X2 + y2 = 1
36 20
[AC] [ALPHA] [X] [x2] [ab/c] [3] [6] [+] [ALPHA] [Y] [x2] [ab/c] [2] [0] [=] (1)
Option (B) is correct
Checking option (C) X2 + y2 = 1
16 9
[AC] [ALPHA] [X] [x2] [ab/c] [1] [6] [+] [ALPHA] [Y] [x2] [ab/c] [9] [=] (21/4)
Option (C) is wrong go to the next option
Checking option (D) X2 + y2 = 1
25 9
[AC] [ALPHA] [X] [x2] [ab/c] [2] [5] [+] [ALPHA] [Y] [x2] [ab /c] [9] [=] (111/25)
Option (D) is wrong
The correct option is (B) to find the foci use option (B) since option (B) is correct to get the foci use c2 = ±√A2 – B2 where A2 = 36 B2 = 20 since using the formula
X2 + y2 = 1
A2 – B2
Calculating c2 = ±√36 – 20 using the denominator, c2 = ±√16 c = ±4 = foci = (4,0), (-4,0)
(7). Find the equation of the circle that passes through the point (2, 1) (0, -3) (4, 3)
(A)X2 + Y2 – 22x – 12y + 27 = 0 (B) X2 + Y2 + 22x – 12y + 27 = 0 (C) X2 + Y2 – 22x + 12y + 27 = 0 (D) X2 + Y2 + 22x + 12y + 27 = 0
Solution:-Using CASIO fx-991MS calculator
Make x = any of the points given, From the first point (2,1) x;. x = 2 y =1
[ON] [2] [SHIFT] [STO] [X] (X=2)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [1] [SHIFT] [STO] [Y] (Y=1)
Tracing the right options, if any of the options gives zero it is correct but if it did not give zero it is wrong
Checking option (A) X2 + Y2 – 22x – 12y + 27 = 0
[AC] [ALPHA] [X] [x2] [+] [ALPHA] [Y] [x2] [-] [2] [2] [ALPHA] [X] [-] [1] [2] [ALPHA] [Y] [+] [2] [7] [=] (-72)
Option (A) is wrong because it did not give zero don’t bother to make x and y = any other points given go to the next option
Checking option (B) X2 + Y2 + 22x – 12y + 27 = 0
[AC] [ALPHA] [X] [x2] [+] [ALPHA] [Y] [x2] [+] [2] [2] [ALPHA] [X] [-] [1] [2] [ALPHA] [Y] [+] [2] [7] [=] (104)
Option (B) is wrong because it did not give zero don’t bother to make x and y = any other points given go to the next option
Checking option (C) X2 + Y2 – 22x + 12y + 27 = 0
[AC] [ALPHA] [X] [x2] [+] [ALPHA] [Y] [x2] [-] [2] [2] [ALPHA] [X] [+] [1] [2] [ALPHA] [Y] [+] [2] [7] [=] (0)
Option (C) is correct on point 1 go to the next point (0,-3) make x = 0 y = -3
[AC] [0] [SHIFT] [STO] [Y] (X=0)
[AC] [(-)] [3] [SHIFT] [STO] [Y] (Y=-3)
Press [↑] [↑] [=] (0)
The second point corresponds go to the next point (4,3) make x = 4 y = 3
[AC] [4] [SHIFT] [STO] [X] (X=4)
[AC] [3] [SHIFT] [STO] [Y] (Y=3)
Press [↑] [↑] [=] (0)
The third point corresponds :. The correct option is “C”
(7). Find the point of intersection of the equation 2x – y = -3 and 3 x + y = 7
(A) 1/5, 23/5 (B) 4/5, 5/23 (C) 4/5,23/5 (D) 23/5, 4/5
Solution:-Using CASIO fx-991MS calculator
Use simultaneous method to solve the following equation
2x – y = -3 -------------------------------(equation 1)
3x + y = 7---------------------------------(equation 2)
Press [ON] [MODE] [MODE] [MODE] [1] [2] (contd)→
2x – y = -3 -------------------------------a1 + b1 = c1
3x + y = 7---------------------------------a2 + b2 = c1
Impute the coefficients a1 = 2 b1 = -1 c1 = -3 a2 = 3 b2 = 1 c2 = 7
→[2] [=] [-] [1] [=] [-] [3] [=] [3] [=] [1] [=] [7] [=] (x=0.8) press [ab/c] (4/5) press [=] or [↓] (y=4.6)
press [ab/c] (43/5) press [SHIFT] [d/c] (23/5) :. X = 4/5 y =23/5
The correct option is “C”
Unforgiveness is a sin, if you don’t forgive; your trespasses (sins) will not be forgiven
Reason. In Mathew 6:14-15- if ye forgive men their trespasses your heavenly father will also forgive your trespasses but if ye forgive not men their trespasses neither will your father forgive your trespasses
Also in Mark 11:25-26- And when ye stand praying forgive if you have ought against any that your father also which is in heaven will forgive your trespasses. But if ye do not forgive, neither will your father which is in heaven forgive your trespasses.
For your heavenly father to forgive your trespasses. You must forgive those that trespass against you including your enemies. In Matthew 5:44-Love your enemies, bless them that curse you, do good to them that hate you, pray for them which despitefully use you and persecute you. As a Christian/Believer of JESUS CHRIST you must forgive your enemies including those that commit evil against you because if you don’t forgive them you are in darkness. In 1 John 2:9-11 – He that saith he is in the light and hateth his brother is in darkness even until now. He that loveth his brother abideth in the light and there is none occasion of stumbling in him. But he that hateth his brother is in darkness and walketh in darkness and knoweth not wither because that darkness has blinded his eyes. A believer will say I am in the light by being a deacon, choir, usher, pastor, evangelist, But know that Christians/believers who is indulge in unforgiveness will not inherit the kingdom of God and they will spend their eternity in hell (the fire that never shall be quenched). Mark 9:43
Know that if you don’t forgive today, your prayers will not be answered. But if you are touched by the word of GOD on unforgiveness and you have make a decision in your heart to forgive whomsoever wronged you, offend you, please make this confession
LORD JESUS, as I come to you, have mercy upon me, as I forgive those that offend me today. Forgive me my trespasses; receive me into your kingdom, IN JESUS NAME AMEN.
NOW: that you have confess this prayer of unforgiveness you are free to confess the next prayer below if you are not
Born-again
if you have not born-again or given your life to Jesus Christ say this prayer “Lord JESUS, as I come to you today, Have mercy upon me, Forgive me all my sins, wash me with your precious blood, save my soul, as I receive you today as my lord and personal savior, write my name in the book of life, IN JESUS NAME AMEN.
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