Find the standard form of the equation of the following conic section.
-center $( - 4 , - 1 ) ; r = \sqrt { 3 }$
A) $( x - 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 9$
B) $( x - 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 3$
C) $( x + 1 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9$
D) $( x + 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 3$

Question

Quizplus · Accepted Answer

The standard form of the equation for a circle is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. Given the center $(-4, -1)$ and $r = \sqrt{3}$, the equation becomes $(x + 4)^2 + (y + 1)^2 = (\sqrt{3})^2$ or $(x + 4)^2 + (y + 1)^2 = 3$, which matches option D.

Find the Standard Form of the Equation of the Following (−4,−1);r=3( - 4 , - 1 ) ; r = \sqrt { 3 }(−4,−1);r=3​

Find the Standard Form of the Equation of the Following $( - 4 , - 1 ) ; r = \sqrt { 3 }$