Question

What is the equation of the circle with center (0, 0) that passes through the point (5, -4)?

Answer 1

The standard form of a circle is $(x-h) ^{2} +(y-k) ^{2} = r^{2}$ where h and k are the center and x and y are the coordinates you're given.  We need to solve for the radius to finish this off correctly.  Filling in, we have $(5-0) ^{2} +(-4-0) ^{2} = r^{2}$ and $25+16= r^{2}$, giving us that $r^{2}=41$.  Therefore, our equation is $x^{2} + y^{2} =41$