Question

Which is an equation of a circle with center (2, -1) that passes through the point (3, 4)?

1. (x + 2)2 + (y - 1)2 = 26
2. (x + 2)2 + (y - 1)2 = 13
3. (x - 2)2 + (y + 1)2 = 26
4. (x - 2)2 + (y + 1)2 = 13

Answer 1

The equation for a circle is (x-h)^2 + (y-k)^2 = r^2. Because we have a center and a coordinate, all we have to solve for is the radius. Fill in the equation like this: (3-2)^2 + (4+1)^2 = r^2. That gives us 1^2 + 5^2 = r^2 and 26=r^2. Now we use that squared radius along with the center to complete the equation for the circle: (x-2)^2 + (y+1)^2 = 26 which is #3 above.