Question

Find the equation for the circle with a diameter whose endpoints are (-5, -3) and (3,2).

Write the standard equation for the circle.

Answer 1

(x +1)^2 +(y +0.5)^2 = 22.25

Explanation:

The center of the circle is the midpoint of the diameter, so is ...

(h, k) = ((-5, -3) +(3, 2))/2 = (-5+3, -3+2)/2 = (-1, -1/2)

The circle formula is then ...

(x -h)^2 +(y -k)^2 = r^2

(x -(-1))^2 +(y -(-1/2))^2 = r^2

We can find r^2 by substituting one of the points for (x, y).

(3 +1)^2 +(2 +1/2)^2 = r^2 = 16 +6.25 = 22.25

Then the circle equation is ...

(x +1)^2 +(y +0.5)^2 = 22.25