Question

Find the​ center-radius form for the circle having the endpoints

left parenthesis 7 comma 4 right parenthesis(7,4)

and

left parenthesis negative 9 comma 6 right parenthesis(−9,6)

of a diameter.

Answer 1

(x +1)² +(y -5)² = 65

Explanation:

The center is the midpoint of the diameter, the average of the end points:

C = ((7, 4) +(-9, 6))/2 = ((7-9)/2, (4+6)/2) = (-1, 5)

The formula for center (h, k) and radius r is ...

(x -h)² +(y -k)² = r²

We can find r² by substituting one of the diameter end points for (x, y) and the center for (h, k).

(7 +1)² +(4 -5)² = r² = 65

Then the circle's equation is ...

(x +1)² +(y -5)² = 65