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

B) $y = 8 + \sqrt { x ^ { 2 } }$ and $- y = - 8 - \sqrt { x ^ { 2 } }$

C) $y = 8 x ^ { 2 } + 8$ and $y = - 8 x ^ { 2 } - 8$

D) $y = 8 \sqrt { x ^ { 2 } + 1 }$ and $y = - 8 \sqrt { x ^ { 2 } + 1 }$

Question

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

B) $y = 8 + \sqrt { x ^ { 2 } }$ and $- y = - 8 - \sqrt { x ^ { 2 } }$

C) $y = 8 x ^ { 2 } + 8$ and $y = - 8 x ^ { 2 } - 8$

D) $y = 8 \sqrt { x ^ { 2 } + 1 }$ and $y = - 8 \sqrt { x ^ { 2 } + 1 }$

Quizplus · Accepted Answer

To graph a hyperbola on a calculator, you need to solve for $y$ in terms of $x$. Starting with $y^2 - 64x^2 = 64$, divide everything by 64 to get $\frac{y^2}{64} - x^2 = 1$. This simplifies to $y^2 = 64x^2 + 64$. Taking the square root of both sides gives $y = \pm \sqrt{64x^2 + 64}$, which simplifies to $y = \pm 8\sqrt{x^2 + 1}$, matching choice D.

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