Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { ( x - 5 ) ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 1$$
A) $y = \frac { 7 \sqrt { 36 - x ^ { 2 } } } { 6 }$ and $y = - \frac { 7 \sqrt { 36 - x ^ { 2 } } } { 6 }$
B) $y = \frac { 7 \sqrt { 900 - x ^ { 2 } } } { 6 }$ and $y = - \frac { 7 \sqrt { 900 - x ^ { 2 } } } { 6 }$
C) $y = \frac { 7 \sqrt { 25 - x ^ { 2 } } } { 6 }$ and $y = - \frac { 7 \sqrt { 25 - x ^ { 2 } } } { 6 }$
D) $y = \frac { 7 \sqrt { - x ^ { 2 } + 10 x + 11 } } { 6 }$ and $y = - \frac { 7 \sqrt { - x ^ { 2 } + 10 x + 11 } } { 6 }$

Question

Quizplus · Accepted Answer

To graph the ellipse, we need to solve the given equation for $y$. The correct transformation involves completing the square for the $x$ term inside the square root, which matches option D. The original equation is $\frac{(x-5)^2}{36} + \frac{y^2}{49} = 1$. Solving for $y$ gives $y = \pm\sqrt{49 - \frac{49(x-5)^2}{36}}$, which simplifies to $y = \pm\frac{7\sqrt{36-(x-5)^2}}{6}$, matching the structure of option D after expanding $(x-5)^2$.

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