Find the standard form of the equation of the ellipse below.
$2 x ^ { 2 } + 8 y ^ { 2 } + 24 x - 64 y + 16 = 0$
A) $\frac { ( x - 6 ) ^ { 2 } } { ( 2 \sqrt { 23 } ) ^ { 2 } } + \frac { ( y + 4 ) ^ { 2 } } { ( \sqrt { 23 } ) ^ { 2 } } = 1$
B) $\frac { ( x + 6 ) ^ { 2 } } { ( 2 \sqrt { 23 } ) ^ { 2 } } + \frac { ( y - 4 ) ^ { 2 } } { ( \sqrt { 23 } ) ^ { 2 } } = 1$
C) $\frac { ( x + 4 ) ^ { 2 } } { ( \sqrt { 23 } ) ^ { 2 } } - \frac { ( y - 6 ) ^ { 2 } } { ( 2 \sqrt { 23 } ) ^ { 2 } } = 1$
D) $\frac { ( x - 4 ) ^ { 2 } } { ( \sqrt { 23 } ) ^ { 2 } } + \frac { ( y + 6 ) ^ { 2 } } { ( 2 \sqrt { 23 } ) ^ { 2 } } = 1$
E) $\frac { ( x - 4 ) ^ { 2 } } { ( 2 \sqrt { 23 } ) ^ { 2 } } - \frac { ( y + 6 ) ^ { 2 } } { ( \sqrt { 23 } ) ^ { 2 } } = 1$

Question

Quizplus · Accepted Answer

The given equation is rearranged and completed to form the standard ellipse equation $\frac{(x+6)^2}{(2\sqrt{23})^2} + \frac{(y-4)^2}{(\sqrt{23})^2} = 1$.

Find the Standard Form of the Equation of the Ellipse 2x2+8y2+24x−64y+16=02 x ^ { 2 } + 8 y ^ { 2 } + 24 x - 64 y + 16 = 02x2+8y2+24x−64y+16=0

Find the Standard Form of the Equation of the Ellipse $2 x ^ { 2 } + 8 y ^ { 2 } + 24 x - 64 y + 16 = 0$