Suppose (9, 14) and (3, −10) are the endpoints of a diameter of a circle. What is the equation of the circle?

The equation of circle is + = 153

Step-by-step explanation:

Given the endpoints of a diameter of a circle: (9,14) and (3,-10)

We know that the equation of a 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

(   ,  )

(   ,  )

(6,2)

Hence (h,k) is (6,2)

Substituting values of (h.k) and (x.y) as (6,2) and (9,14) respectively in equation of circle, we get

+ =

= 153

Substituting the values of (h,K) and  , we get the equation of circle as

+ = 153

Hence the equation of circle is + = 153