Question

Find the equation of the circle with center at (-3, 1) and through the point (2, 13).

Answer 1

The center of a circle has the equation \((x - h)^2 + (y - k)^2 = r^2\). The center is (-h, -k). After finding what h and k are, find what r is by finding the distance between the points (-3, 1) and (2, 13).

Answer 2

but how do you do that..?

Answer 3

Basically, plug in the h and k into the equation and simplify it.
\[(x - (-3))^2 + (y - 1)^2 = r^2 \implies (x + 3)^2 + (y - 1)^2 = r^2\]Now, use the distance formula to find \(r^2\)
\[r^2 = (x_1 - x_2)^2 + (y_1 - y_2)^2\]Can you figure out what r is?