Determine the two equations necessary to graph the hyperbola with a graphing calculator.
-$$\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 144 } = 1$$
A) $y = \frac { 12 \sqrt { x ^ { 2 } } - 7 } { 7 }$ and $y = - \frac { 12 \sqrt { x ^ { 2 } } - 7 } { 7 }$
B) $y = \frac { 7 \sqrt { x ^ { 2 } + 49 } } { 12 }$ and $y = - \frac { 7 \sqrt { x ^ { 2 } + 49 } } { 12 }$
C) $y = \frac { 12 \sqrt { x ^ { 2 } - 49 } } { 7 }$ and $y = - \frac { 12 \sqrt { x ^ { 2 } - 49 } } { 7 }$
D) $y = \frac { 7 \sqrt { x ^ { 2 } - 49 } } { 12 }$ and $y = - \frac { 7 \sqrt { x ^ { 2 } - 49 } } { 12 }$

Question

Quizplus · Accepted Answer

To graph the given hyperbola $\frac{x^2}{49} - \frac{y^2}{144} = 1$ on a calculator, we need to solve for $y$ in terms of $x$. Rearranging the equation gives $y^2 = \frac{x^2}{49} \times 144 - 144$, which simplifies to $y^2 = \frac{144x^2}{49} - 144$. Taking the square root of both sides gives $y = \pm \sqrt{\frac{144x^2}{49} - 144}$, which simplifies to $y = \pm \frac{12}{7}\sqrt{x^2 - 49}$, matching choice C.

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