Find the equation of the circle with a radius of 9 and its center at the intersection of $3 x + y = 5$ and $2 x -$ $3 y = - 4$.
A) $( x - 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 9$
B) $\quad ( x + 1 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 81$
C) $( x + 1 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 9$
D) $\quad ( x - 1 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 81$
E) $\quad ( x - 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 81$

Question

Quizplus · Accepted Answer

The center of the circle is found by solving the system of equations $3x + y = 5$ and $2x - 3y = -4$. Solving this system gives $x = 1$ and $y = 2$. The radius is 9, so the equation of the circle is $(x - 1)^2 + (y - 2)^2 = 9^2$, which simplifies to $(x - 1)^2 + (y - 2)^2 = 81$.

Find the Equation of the Circle with a Radius of 9