Question

Find an equation of the circle that has center .(-4, -3) and passes through (5,5).

Answer 1

Answer:

(x+4)^2 + (y+3)^2 = 145

Explanation:

Using the circle equation (x-h)^2 + (y-k)^2 = r^2

We know that the center of the circle is (h,k). But to find the working radius that passes through the desired point, substitute that point into the x, and y, and add them up.

(x+4)^2 + (y+3)^2 = (5,5) → (5+4)^2 + (5+3)^2 = 9^2 + 8^2 = 81 + 64 = 145

*Magic*

Now try and substitute the other point into the equation

(5,5) → (x+4)^2 + (y+3)^2 = 145 → (5+4)^2 + (5+3)^2 = 145 → 9^2 + 8^2 = 145 → 81 + 64 = 145 → 145 = 145