Question

The points J (-13,10) and K(-1,-6) are endpoints of a diameter of circle G. What is the equation of circle G?

A. (x - 7)2 + (y+ 2)2 = 400
B. (x-7) + (y+ 2)2 = 100
C (x+7)2 +(y- 2)2 = 400
D (x+7)2+(y -2)2 = 100 E (x+ 7)2 + (y- 2)2 = 28

Answer 1

(x + 7)2 + (y − 2)2 = 100

Explanation:

I just solved this

Answer 2

The correct answer is D

The equation of a circle is (x-h)^2 + (y-k)^2 = r^2

to find (h,k), you find the middle of the circle, in this scenario you do so by finding the middle of the diameter, a line that goes through the center of the circle.

To find the X value of the midpoint, add both x values together and divide by 2 and repeat for y

-13 + -1 = -14
-14/2 =-7

10+ -6 = 4
4/2 = 2

therefore (h,k) = ( -7, 2 )

Next plug these values in the equation of a circle

(x-h)^2 + (y-k)^2 = r^2

becomes

(x- (-7)) ^2 + (y-(2)) ^2 = r^2

to find r, use the distance formula to find the length of the diameter, 20, and divide by 2


plug 10 in for r and you get 100

(x+7)^2 + (y-2)^2 = 100

sorry for the late response