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

Read the explanation for the answers

Explanation:

To find the midpoint, you simply need to find the average of the two endpoints. The average of 10.5 and 5.5 is 8, and the average of 4 and 4 is 4. Therefore, the center of the circle is at (4,8). The radius is the distance from the center to either of these points, or 8-5.5=2.5 units. And finally, the formula for the circle in standard form is
`(y-8)^2+(x-4)^2=6.25`. Hope this helps!