Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 25 } = 1$$
A) $y = \sqrt { \frac { 180 - x ^ { 2 } } { 6 } }$ and $y = - \sqrt { \frac { 150 - x ^ { 2 } } { 6 } }$
B) $y = \sqrt { \frac { 150 - x ^ { 2 } } { 5 } }$ and $y = - \sqrt { \frac { 150 - x ^ { 2 } } { 5 } }$
C) $y = \frac { 5 \sqrt { 36 - x ^ { 2 } } } { 36 }$ and $y = - \frac { 5 \sqrt { 36 - x ^ { 2 } } } { 36 }$
D) $y = \frac { 5 \sqrt { 36 - x ^ { 2 } } } { 6 }$ and $y = - \frac { 5 \sqrt { 36 - x ^ { 2 } } } { 6 }$

Question

Quizplus · Accepted Answer

To graph the ellipse, we need to solve for $y$ in terms of $x$. Starting with $\frac{x^2}{36} + \frac{y^2}{25} = 1$, we solve for $y^2$, getting $y^2 = 25(1 - \frac{x^2}{36})$. Taking the square root of both sides gives $y = \pm\sqrt{25(1 - \frac{x^2}{36})}$, which simplifies to $y = \pm\frac{5\sqrt{36 - x^2}}{6}$, matching choice D.

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