Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$$
A) $y = \sqrt { \frac { 100 - x ^ { 2 } } { 5 } }$ and $y = - \sqrt { \frac { 80 - x ^ { 2 } } { 5 } }$
B) $y = \frac { 4 \sqrt { 25 - x ^ { 2 } } } { 25 }$ and $y = - \frac { 4 \sqrt { 25 - x ^ { 2 } } } { 25 }$
C) $y = \sqrt { \frac { 80 - x ^ { 2 } } { 4 } }$ and $y = - \sqrt { \frac { 80 - x ^ { 2 } } { 4 } }$
D) $y = \frac { 4 \sqrt { 25 - x ^ { 2 } } } { 5 }$ and $y = - \frac { 4 \sqrt { 25 - x ^ { 2 } } } { 5 }$

Question

Quizplus · Accepted Answer

To graph the ellipse, solve for $y$ in terms of $x$. Starting with $\frac{x^2}{25} + \frac{y^2}{16} = 1$, multiply both sides by 16 to get $y^2 = 16(1 - \frac{x^2}{25})$. Taking the square root of both sides gives $y = \pm 4\sqrt{1 - \frac{x^2}{25}}$, which simplifies to $y = \pm \frac{4\sqrt{25 - x^2}}{5}$, matching choice D.

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