# math-equation of circle

Write the standard form of the equation of the circle that passes through the points at (4,5) (-2, 3), and (-4,-3).
a. (x-5)^2+(y+4)^2=49
b. (x-3)^2+(y+2)^2=50
c. (x+4)^2+(y-2)^2=36
d. (x-2)^2+(y+2)^2=25

I'm having trouble with solving for the variables...after I make the system of equations, I use elimination and wind up with odd numbers (1/9 for E, 307/9 for F).
If somebody who is good at this could show me their steps it would really help me understand what I'm doing wrong.
Thanks so much in advance, I really appreciate the help! MUCH needed!

1. 👍
2. 👎
3. 👁
1. Since this is multiple choice, the quickest way to determine the correct solution would be to plug in the given coordinates into each of the solutions.

1. 👍
2. 👎
2. Well, call center at (xc,yc) and radius r
then
(x-xc)^2 + (y-yc)^2 = r^2
distance from center to those points is the same = r
(4-xc)^2 + (5-yc)^2 = r^2
(-2-xc)^2 + (3-yc^2) = r^2
(-4-xc)^2 + (-3-yc^2) = r^2

16-8xc+xc^2+25-10yc+yc^2 = r^2
4+4xc+xc^2+9-6yc+yc^2 = r^2
16+8xc+xc^2+9+6yc+yc^2 = r^2

-8xc+xc^2-10yc+yc^2 = r^2-41
+4xc+xc^2-6yc+yc^2 = r^2-13
+8xc+xc^2+6yc+yc^2 = r^2-25

12 xc +4 yc = 28 changing sign of first and adding to second
4xc +12 yc = -12 changing sign of second and adding to third

12 xc +4 yc = 28
12 xc +36 yc = -36
-32yc = 64
yc = -2

ok, take it from there

1. 👍
2. 👎
3. of course it has to be b or d, but solve for xc to tell
4 xc + 12(-2) = -12
4 xc = 12
xc = 3
so center at
(3,-2)
and of form
(x-3)^2 +(y+2)^2 = r^2

1. 👍
2. 👎
4. Thanks Damon!!
This helped a lot...I was totally backwards on some things.

1. 👍
2. 👎

## Similar Questions

1. ### geometry

Write the standard equation for the circle center (-6,-8), that passes through (0,0). I know that the formula would leave the 1qstr part as (x+6)+(y+8) I'm not sure about the radius when it goes through (0,0)

2. ### algebra 1

Write an equation in standard form of the line that passes through the given points (2,6)(3,8) -2x+y=2

3. ### Math(check)

1)Find the range of the relation [(-1,4)},(2,5),(3,5)}.Then determine whether the relation is a funtion. 4,5,5 is the range 4,5 is a function 2)Find f(-1),if f(x)= x^2-6x/x+2 (-1)^2-6(-1)/-1+2 1+6/-1+2 7/1 =7 3)Find f(a),if f(t)=

4. ### Geometry

Write the equation of circle O centered at origin that passes through (9,-2) Circle B with center (0,-2) that passes through (-6,0) >For circle B, is the radius 6 in this case? So equation would be x^2+(x+2)^2=36, correct? If this

1. ### geometry

in the coordinate plane, the points (2,2) and (2,12) are the endpoints of a diameter of a circle. what is the equation of the circle in standard form?

2. ### Mathematics

Can someone check my answers? 1. For the data in the table, does y vary directly with X? If it does write an equation for the direct variation.(X,y) (8,11) (16,22) (24,33) Yes y=2.75x Yes y=0.6875x*** Yes y=1.375x No y does not

3. ### Algebra 2 H

Write an equation in standard form for the parabola that passes through the points: (-2, 64), (3, -16), (7, 28)

4. ### pre calculus

Write the equation of the circle in standard form. Find the center, radius, intercepts, and graph the circle. x^2+y^2-12x-4x+36=0 How on earth do I do this?

1. ### Math

1. Find the slope of the line that passes through the points (-1, 2), (0, 5). 2. Suppose y varies directly with x, and y = 15 and x = 5. Write a direct variation equation that relates x and y. What is the value of y when x = 9? 3.