Identify the conic by writing the equation in standard form. $10 y ^ { 2 } - 20 x ^ { 2 } + 80 y + 360 x - 1485 = 0$
A) $\frac { ( y - 4 ) ^ { 2 } } { \frac { 5 } { 2 } } - \frac { ( x - 9 ) ^ { 2 } } { \frac { 5 } { 4 } } = 1$ ; hyperbola
B) $\frac { ( y + 4 ) ^ { 2 } } { \frac { 5 } { 2 } } - \frac { ( x - 9 ) ^ { 2 } } { \frac { 5 } { 4 } } = 1$ ; hyperbola
C) $\frac { ( y + 4 ) ^ { 2 } } { \frac { 97 } { 2 } } - \frac { ( x - 9 ) ^ { 2 } } { \frac { 97 } { 4 } } = 1$ ; hyperbola
D) $\frac { ( y + 4 ) ^ { 2 } } { \frac { 149 } { 5 } } + \frac { ( x - 9 ) ^ { 2 } } { \frac { 149 } { 10 } } = 1$ ; ellipse
E) $\frac { ( y - 4 ) ^ { 2 } } { \frac { 149 } { 5 } } + \frac { ( x - 9 ) ^ { 2 } } { \frac { 149 } { 10 } } = 1$ ; ellipse

Question

Quizplus · Accepted Answer

The given equation is a hyperbola. By completing the square for both $x$ and $y$, the equation can be rewritten in the standard form of a hyperbola, which matches option B.

Identify the Conic by Writing the Equation in Standard Form 10y2−20x2+80y+360x−1485=010 y ^ { 2 } - 20 x ^ { 2 } + 80 y + 360 x - 1485 = 010y2−20x2+80y+360x−1485=0

Identify the Conic by Writing the Equation in Standard Form $10 y ^ { 2 } - 20 x ^ { 2 } + 80 y + 360 x - 1485 = 0$