Determine the two equations necessary to graph the hyperbola with a graphing calculator.
-$$y ^ { 2 } - 64 x ^ { 2 } = 64$$
A) $y = 8 \sqrt { x ^ { 2 } + 1 }$ and $y = - 8 \sqrt { x ^ { 2 } + 1 }$
B) $y = 8 + \sqrt { x ^ { 2 } }$ and $- y = - 8 - \sqrt { x ^ { 2 } }$
C) $y = 8 + \sqrt { x ^ { 2 } }$ and $y = 8 - \sqrt { x ^ { 2 } }$
D) $y = 8 x ^ { 2 } + 8$ and $y = - 8 x ^ { 2 } - 8$

Question

Quizplus · Accepted Answer

To graph the given hyperbola $y^2 - 64x^2 = 64$, we first solve for $y$ to get it in a form that can be graphed as two functions. Dividing the entire equation by 64 gives $\frac{y^2}{64} - \frac{64x^2}{64} = 1$, simplifying to $\frac{y^2}{64} - x^2 = 1$. Solving for $y$, we get $y^2 = 64x^2 + 64$, and taking the square root of both sides gives $y = \pm \sqrt{64x^2 + 64}$. Factoring out the 64 inside the square root gives $y = \pm \sqrt{64(x^2 + 1)}$, which simplifies to $y = \pm 8\sqrt{x^2 + 1}$, matching choice A.

Determine the Two Equations Necessary to Graph the Hyperbola with a Graphing