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 ______ .

Answer 1

The center of the circle is at the point ? , and its radius is 2.5 units. The equation of this circle in standard form is (x - 4)² + (y - 8)² = 6.25.

Explanation:

Answer 2

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
((x1 +x2)/2 , (y1+y2)/2).. Just substitute them for the solution


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