Answer:
The equation of circle is +
= 52
Step-by-step explanation:
Given the endpoints of diameter of a circle: (-16,-16) and (-4,-8)
We know that the equation of circle is given by
+
=
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
( ,
)
( ,
)
(-10, -12)
Hence (h,k) is (-10,-12)
Substituting values of (h.k) and (x.y) as (-10,-12) and (-4,-8) respectively in equation of circle, we get
+
=
= 52
Substituting values of (h.k) and , we get the equation of circle as
+
= 52
Hence the equation of circle is +
= 52