Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { ( x - 2 ) ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$$
A)$y = \frac { 5 \sqrt { 64 - x ^ { 2 } } } { 8 }$ and $y = - \frac { 5 \sqrt { 64 - x ^ { 2 } } } { 8 }$

B) $y = \frac { 5 \sqrt { - x ^ { 2 } + 4 x + 60 } } { 8 }$ and $y = - \frac { 5 \sqrt { - x ^ { 2 } + 4 x + 60 } } { 8 }$

C) $y = \frac { 5 \sqrt { 256 - x ^ { 2 } } } { 8 }$ and $y = - \frac { 5 \sqrt { 256 - x ^ { 2 } } } { 8 }$

D) $y = \frac { 5 \sqrt { 4 - x ^ { 2 } } } { 8 }$ and $y = - \frac { 5 \sqrt { 4 - x ^ { 2 } } } { 8 }$

Question

Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { ( x - 2 ) ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$$
A)$y = \frac { 5 \sqrt { 64 - x ^ { 2 } } } { 8 }$ and $y = - \frac { 5 \sqrt { 64 - x ^ { 2 } } } { 8 }$

B) $y = \frac { 5 \sqrt { - x ^ { 2 } + 4 x + 60 } } { 8 }$ and $y = - \frac { 5 \sqrt { - x ^ { 2 } + 4 x + 60 } } { 8 }$

C) $y = \frac { 5 \sqrt { 256 - x ^ { 2 } } } { 8 }$ and $y = - \frac { 5 \sqrt { 256 - x ^ { 2 } } } { 8 }$

D) $y = \frac { 5 \sqrt { 4 - x ^ { 2 } } } { 8 }$ and $y = - \frac { 5 \sqrt { 4 - x ^ { 2 } } } { 8 }$

Quizplus · Accepted Answer

To graph the given ellipse equation, we need to solve for $y$ in terms of $x$. Starting with $\frac{(x-2)^2}{64} + \frac{y^2}{25} = 1$, we isolate $y^2$ and take the square root to solve for $y$, obtaining two equations (positive and negative square roots). The correct manipulation involves completing the square for $x$ and simplifying, leading to the equations in choice B, which correctly accounts for the shift and scaling of the ellipse.

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