Question

Which is an equation of a circle with center (-5, -7) that passes through the point (0, 0)?

Answer 1

First find the radius of the circle:
$r = \sqrt{(-5 - 0)^{2} + (-7 - 0)^{2} } \\ r = \sqrt{(-5)^{2} + (-7)^{2} } \\ r = \sqrt{25 + 49} \\ r \sqrt{74} \\ r^{2} = 74 \\ (x - (-5))^{2} + (y - (-7))^{2} = 74 \\ (x + 5)^{2} + (y + 7)^{2} = 74$