Identify the conic by writing the equation in standard form. $8 x ^ { 2 } + 8 y ^ { 2 } + 32 x + 144 y + 520 = 0$
A) $$\frac { ( x + 2 ) ^ { 2 } } { \frac { 69 } { 8 } } + \frac { ( y + 9 ) ^ { 2 } } { \frac { 69 } { 8 } } = 1$$ ;ellipse
B) $\frac { ( x + 2 ) ^ { 2 } } { \frac { 11 } { 8 } } + \frac { ( y + 9 ) ^ { 2 } } { \frac { 11 } { 8 } } = 1$ ;ellipse
C) $( 8 x + 2 ) ^ { 2 } + ( 8 y + 9 ) ^ { 2 } = 320$ ;circle
D) $( x + 2 ) ^ { 2 } + ( y + 9 ) ^ { 2 } = 40$ ;circle
E) $( x + 2 ) ^ { 2 } + ( y + 9 ) ^ { 2 } = 20$ ;circle

Question

Quizplus · Accepted Answer

The given equation can be rewritten by completing the square for both x and y terms, resulting in $(x + 2)^2 + (y + 9)^2 = 20$, which is the equation of a circle with center (-2, -9) and radius $\sqrt{20}$.

Identify the Conic by Writing the Equation in Standard Form 8x2+8y2+32x+144y+520=08 x ^ { 2 } + 8 y ^ { 2 } + 32 x + 144 y + 520 = 08x2+8y2+32x+144y+520=0

Identify the Conic by Writing the Equation in Standard Form $8 x ^ { 2 } + 8 y ^ { 2 } + 32 x + 144 y + 520 = 0$