Find an equation of the circle whose diameter has endpoints , 6−2 and , −4−4 .
Accepted Solution
A:
If you need just the answer, it's in bold at the bottom. Otherwise, the process for how I got there is below.
In order to find the equation, we first find the midpoint. This will give us the center of the two endpoints. Then, we do the distance formula to find how many units there are between the endpoints and cut it in half to find the radius. After, we plug in the new information into the equation format of the circle.
So the distance between the two endpoints (the diameter) is 2√26 units long. We divide this by 2 and get the measurement of the radius. The radius is √26 units long.
Now we plug in to the equation of a circle:
(x - h)² + (y - k)² = r²
The center of the circle is represented by the ordered pair (h, k) and the radius is represented by r.
So your equation becomes: (x - 1)² + (y + 3)² = (√26)²