Write an equation of a circle centered at $\left( - \frac { 2 } { 3 } , \frac { 1 } { 3 } \right)$ with a radius of $3 \sqrt { 5 }$.
A) $\left( x - \frac { 2 } { 3 } \right) ^ { 2 } + \left( y + \frac { 1 } { 3 } \right) ^ { 2 } = 45$
B) $\left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \left( y - \frac { 1 } { 3 } \right) ^ { 2 } = 45$
C) $\left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \left( y - \frac { 1 } { 3 } \right) ^ { 2 } = 3 \sqrt { 5 }$
D) $\left( x - \frac { 1 } { 3 } \right) ^ { 2 } + \left( y + \frac { 2 } { 3 } \right) ^ { 2 } = 3 \sqrt { 5 }$

Question

Quizplus · Accepted Answer

The equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. Here, the center is $(- \frac{2}{3}, \frac{1}{3})$ and the radius is $3\sqrt{5}$, so the equation is $(x + \frac{2}{3})^2 + (y - \frac{1}{3})^2 = (3\sqrt{5})^2 = 45$.

Write an Equation of a Circle Centered At (−23,13)\left( - \frac { 2 } { 3 } , \frac { 1 } { 3 } \right)(−32​,31​)

Write an Equation of a Circle Centered At $\left( - \frac { 2 } { 3 } , \frac { 1 } { 3 } \right)$