Find an equation of the circle with the given characteristics.
-$( 0,12 )$ and radius $\sqrt { 6 }$
A) $x ^ { 2 } + ( y + 12 ) ^ { 2 } = \sqrt { 6 }$
B) $( y + 12 ) ^ { 2 } = 6$
C) $( y - 12 ) ^ { 2 } = \sqrt { 6 }$
D) $x ^ { 2 } + ( y - 12 ) ^ { 2 } = 6$

Question

Quizplus · Accepted Answer

The general equation for a circle with center $(h, k)$ and radius $r$ is $(x - h)^2 + (y - k)^2 = r^2$. Given the center $(0, 12)$ and radius $\sqrt{6}$, the equation becomes $x^2 + (y - 12)^2 = (\sqrt{6})^2$, which simplifies to $x^2 + (y - 12)^2 = 6$, matching option D.

Find an Equation of the Circle with the Given Characteristics (0,12)( 0,12 )(0,12)

Find an Equation of the Circle with the Given Characteristics $( 0,12 )$