Determine the center and radius of the circle.
-$$( x + 2 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 45$$
A) Center: $( - 2,3 )$; Radius: $3 \sqrt { 5 }$
B) Center: $( - 2,3 )$; Radius: 45
C) Center: $( 2 , - 3 )$; Radius: $3 \sqrt { 5 }$
D) Center: $( 2 , - 3 )$; Radius: 45

Question

Quizplus · Accepted Answer

The equation of a circle in the form $(x - h)^2 + (y - k)^2 = r^2$ has a center at $(h, k)$ and a radius of $r$. The given equation $(x + 2)^2 + (y - 3)^2 = 45$ matches this form with $h = -2$, $k = 3$, and $r^2 = 45$, which means $r = \sqrt{45} = 3\sqrt{5}$.

Determine the Center and Radius of the Circle (x+2)2+(y−3)2=45( x + 2 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 45(x+2)2+(y−3)2=45

Determine the Center and Radius of the Circle $( x + 2 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 45$