Question

The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).

The center of the circle is at the point , and its radius is units. The equation of this circle in standard form is what?

Answer 1

Answer and Step-by-step explanation:

The longest chord on the circle is the diameter, and the center of the circle is the midpoint of the diameter.

Use the midpoint formula to find the center

the x-coordinates are the same, so you can just subtract the y-coordinates to find the radius.

10.5 - 8 = 2.5

The equation of the circle is (x - h)² + (y - k)² = r² where r is the radius and (h, k) is the center.

(x - 4)² + (y - 8)² = 6.25

Answer 2

center is midpoint of those 2 segments
which is at (4,8)
the distance between center and a point is 2.5 units
so

if center is (h,k) and radius is r then equation is
(x-h)²+(y-k)²=r²
so
center is (4,8) and radius is 2.5
(x-4)²+(y-8)²=2.5²