Find the equation of the circle with a radius of 9 and its center at the intersection of $5 x + y = 20$ and $2 x -$ $3 y = - 9$.
A) $\quad ( x - 3 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$
B) $\quad ( x - 3 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 81$
C) $\quad ( x + 3 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 81$
D) $\quad ( x + 3 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 9$
E) $\quad ( x - 3 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 81$

Question

Quizplus · Accepted Answer

The intersection of the lines $5x + y = 20$ and $2x - 3y = -9$ is the center of the circle. Solving these equations simultaneously gives the center as $(3, 5)$. The equation of a circle with center $(h, k)$ and radius $r$ is $(x - h)^2 + (y - k)^2 = r^2$. With center $(3, 5)$ and radius 9, the equation is $(x - 3)^2 + (y - 5)^2 = 81$.

Find the Equation of the Circle with a Radius of 9