Question

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

Answer 1

http://www.mathwarehouse.com/geometry/circle/images/equation-of-circle/general-formula-equation-of-circle.png

what do you think?

Answer 2

so you can pretty much see the (h, k) in the equation
so what's the radius?

well, notice that it says \(\bf \color{blue}{\text{passes through the point (0, 0)}}\) , meaning if you were to draw a straight line, from the center to THAT POINT, you'd get your radius

so what's that distance? well \(\bf \text{distance between 2 points}\\
d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

Answer 3

what did you get for the radius?

Answer 4

\(\bf d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\\
\textit{2 points of (-5, -7) and (0, 0)}\\
d = \sqrt{(0-(-5))^2 + (0-(-7))^2}\)

Answer 5

74.

Answer 6

so yes, the radius is \(\bf \sqrt{74}\)

so use that in your equation for your circle, keep in mind that \(\bf r = \sqrt{74} \implies r^2 = (\sqrt{74})^2 \implies r^2 = \sqrt{74^2} \implies r^2 = 74\)