Determine the two equations necessary to graph the hyperbola with a graphing calculator.
-$$y ^ { 2 } - 16 x ^ { 2 } = 16$$
A) $\mathrm { y } = 4 + \sqrt { \mathrm { x } ^ { 2 } }$ and $- \mathrm { y } = - 4 - \sqrt { \mathrm { x } ^ { 2 } }$
B) $y = 4 x ^ { 2 } + 4$ and $y = - 4 x ^ { 2 } - 4$
C) $y = 4 \sqrt { x ^ { 2 } + 1 }$ and $y = - 4 \sqrt { x ^ { 2 } + 1 }$
D) $y = 4 + \sqrt { x ^ { 2 } }$ and $y = 4 - \sqrt { x ^ { 2 } }$

Question

Quizplus · Accepted Answer

To graph the given hyperbola $y^2 - 16x^2 = 16$ on a calculator, we need to solve for $y$ in terms of $x$. Rearranging the equation gives $y^2 = 16x^2 + 16$, and taking the square root of both sides yields $y = \pm \sqrt{16x^2 + 16}$. Factoring out the 16 inside the square root gives $y = \pm 4\sqrt{x^2 + 1}$, which matches the equations in choice C.

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