Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { ( x - 3 ) ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 64 } = 1$$
A) $y = \frac { 8 \sqrt { 9 - x ^ { 2 } } } { 9 }$ and $y = - \frac { 8 \sqrt { 9 - x ^ { 2 } } } { 9 }$
B) $y = \frac { 8 \sqrt { - x ^ { 2 } + 6 x + 72 } } { 9 }$ and $y = - \frac { 8 \sqrt { - x ^ { 2 } + 6 x + 72 } } { 9 }$
C) $y = \frac { 8 \sqrt { 81 - x ^ { 2 } } } { 9 }$ and $y = - \frac { 8 \sqrt { 81 - x ^ { 2 } } } { 9 }$
D) $y = \frac { 8 \sqrt { 729 - x ^ { 2 } } } { 9 }$ and $y = - \frac { 8 \sqrt { 729 - x ^ { 2 } } } { 9 }$

Question

Quizplus · Accepted Answer

To graph the ellipse, we need to solve the given equation for $y$. The correct transformation involves moving the $x$ term to the other side and taking the square root, accounting for both positive and negative roots. The correct transformation should also correctly handle the translation of the ellipse along the x-axis (shifting by 3 units to the right) and the scaling factors for $x$ and $y$. The correct equations are obtained by isolating $y$ and considering the horizontal shift of the ellipse, which leads to the expression inside the square root being $-x^2 + 6x + 72$, correctly reflecting the translation and scaling of the ellipse.

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