1. What is the equation of the circle with center (-4,-3) that passes through the point (6,2)?

Question

A. (x-4)^2+(y-3)^2=25
B. (x-4)^2+(y-3)^2=125
C. (x+4)^2+(y+3)^2=25***
D. (x+4)^2+(y+3)^2=125

I think the answer is C but I'm not sure. Can someone help tell me if I'm correct or not.

Answer 1

The standard form equation of a circle:

( x - a ) ^ 2 + ( y - b ) ^ 2 = r ^ 2

a and b are the x and y coordinates of the center of the circle.

r = the radius of the circle.

In this case:

a = - 4 , b = - 3

[ x - ( - 4 ) ] ^ 2 + [ y - ( - 3 ) ] ^ 2 = r ^ 2

( x + 4 ) ^ 2 + ( y + 3 ) ^ 2 = r ^ 2

For x = 6 , y = 2

( x + 4 ) ^ 2 + ( y + 3 ) ^ 2 = r ^ 2

( 6 + 4 ) ^ 2 + ( 2 + 3 ) ^ 2 = r ^ 2

10 ^ 2 + 5 ^ 2 = r ^ 2

100 + 25 = r ^ 2

125 = r ^ 2

r ^ 2 = 125

The equation of the circle:

( x + 4 ) ^ 2 + ( y + 3 ) ^ 2 = 125

Answer D.