Find the center and foci of the following ellipse.
$$4 x ^ { 2 } + 8 y ^ { 2 } - 16 x + 32 y + 32 = 0$$
A) Center: $( - 2,2 )$
Foci: $( - 2 + \sqrt { 2 } , 2 ) , ( - 2 - \sqrt { 2 } , 2 )$
B) Center: $( 2 , - 2 )$
Foci: $( 2 + \sqrt { 2 } , - 2 ) , ( 2 - \sqrt { 2 } , - 2 )$
C) Center: $( 2 , - 2 )$
Foci: $( 2 , - 2 + \sqrt { 2 } ) , ( 2 , - 2 - \sqrt { 2 } )$
D) Center: $( - 2,2 )$
Foci: $( - 2,2 + \sqrt { 2 } ) , ( - 2,2 - \sqrt { 2 } )$
E) Center: $( - 2,2 )$
Foci: $( - 2 + \sqrt { 6 } , 2 ) , ( - 2 - \sqrt { 6 } , - 2 )$

Question

Quizplus · Accepted Answer

The given equation can be rewritten in standard form by completing the square: $(x-2)^2/8 + (y+2)^2/4 = 1$. The center is $(2, -2)$. The distance to the foci is $\sqrt{a^2 - b^2} = \sqrt{8 - 4} = \sqrt{4} = 2$, so the foci are $(2 \pm \sqrt{2}, -2)$.

Find the Center and Foci of the Following Ellipse 4x2+8y2−16x+32y+32=04 x ^ { 2 } + 8 y ^ { 2 } - 16 x + 32 y + 32 = 04x2+8y2−16x+32y+32=0

Find the Center and Foci of the Following Ellipse $4 x ^ { 2 } + 8 y ^ { 2 } - 16 x + 32 y + 32 = 0$