Find the equation of the circle with a radius of 5 and its center at the intersection of $5 x + y = 22$ and $5 x -$ $5 y = 10$.
A) $( x - 4 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 25$
B) $( x - 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25$
C) $( x + 4 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 5$
D) $( x - 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 5$
E) $( x + 4 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 25$

Question

Quizplus · Accepted Answer

To find the center of the circle, solve the system of equations $5x + y = 22$ and $5x - 5y = 10$. Adding the equations eliminates $y$, giving $10x = 32$, so $x = 3.2$ or $x = 16/5$. Substituting $x$ back into one of the original equations to solve for $y$ gives $y = 2$. Thus, the center is at $(16/5, 2)$ or simplified to $(3.2, 2)$. The radius is given as 5, so the equation of the circle is $(x - 3.2)^2 + (y - 2)^2 = 5^2$ or $(x - 4)^2 + (y - 2)^2 = 25$, matching choice B.

Find the Equation of the Circle with a Radius of 5