Convert the equation to the standard form for a hyperbola by completing the square.
-$$y ^ { 2 } - 4 x ^ { 2 } - 2 y - 8 x - 7 = 0$$
A) $\frac { ( y - 2 ) ^ { 2 } } { 4 } - ( x + 2 ) ^ { 2 } = 1$
B) $( x + 1 ) ^ { 2 } - \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$
C) $\frac { ( y - 1 ) ^ { 2 } } { 4 } - ( x + 1 ) ^ { 2 } = 1$
D) $\frac { ( x - 1 ) ^ { 2 } } { 4 } - ( y + 1 ) ^ { 2 } = 1$

Question

Quizplus · Accepted Answer

To convert the given equation to the standard form of a hyperbola, we complete the square for both $y$ and $x$. For $y$, we have $y^2 - 2y$, which completes to $(y-1)^2 - 1$. For $x$, we have $-4x^2 - 8x$, which completes to $-4((x+1)^2 - 1)$. Substituting these back into the equation and simplifying gives $\frac{(y-1)^2}{4} - (x+1)^2 = 1$.

Convert the Equation to the Standard Form for a Hyperbola y2−4x2−2y−8x−7=0y ^ { 2 } - 4 x ^ { 2 } - 2 y - 8 x - 7 = 0y2−4x2−2y−8x−7=0

Convert the Equation to the Standard Form for a Hyperbola $y ^ { 2 } - 4 x ^ { 2 } - 2 y - 8 x - 7 = 0$