The endpoints of the diameter of a circle are (−2, −3) and (4, −1). Which equation represents the circle?

The equation of circle is + = 18

Step-by-step explanation:

Given the endpoints of the diameter of a circle: (-2,-3) and (4,-1)

We know that the equation of circle is

+ =

where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.

To find (h,k): the center is midpoint of diameter

Midpoint of diameter with end points (x1,y1) and (x2,y2) is given by

(   ,  )

( ,  )

(1,2)

Hence (h,k) is (1,2)

Substituting values of (h.k) and (x.y) as (1,2) and (4,-1) respectively in equation of circle, we get

+ =

= 18

Now substituting values of (h,k) and in equation of circle, we get

+ = 18

Hence the equation of circle is + = 18