Question

Find an equation for the circle that has center (−3, 4) and passes through the point (4, −2).

Answer 1

First use the coordinate of the center to start building your equation. The equation of a circle recall is
${(x - h)}^{2} + {(y - k)}^{2} = {r}^{2}$
With the center point being (h,k).

Once you put in the centers coordinates, your equation should be,
${(x + 3)}^{2} + {(y - 4)}^{2} = {r}^{2}$
However we still need to find the radius. We can do this using the second point given, by putting it into the equation and solving for the radius.
${( 4 + 3)}^{2} + {( - 2 - 4)}^{2} = {r}^{2}$
Solving this gives us the final part of the equation.
$85 = {r}^{2}$
And we can finally put our full equation together,
${(x + 3)}^{2} + {(y - 4)}^{2} = 85$