Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { x ^ { 2 } } { 16 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 1$$
A) $y = \frac { 20 - 5 \sqrt { 16 - x ^ { 2 } } } { 4 }$ and $y = \frac { 5 \sqrt { 16 - x ^ { 2 } } + 20 } { 4 }$
B) $y = \frac { 5 \sqrt { 400 - 25 x ^ { 2 } } } { 20 }$ and $y = - \frac { 5 \sqrt { 400 - 25 x ^ { 2 } } } { 20 }$
C) $y = \frac { \sqrt { 400 - 25 x ^ { 2 } } } { 4 }$ and $y = - \frac { \sqrt { 400 - 25 x ^ { 2 } } } { 4 }$
D) $y = \frac { \sqrt { 800 - 25 x ^ { 2 } } } { 4 }$ and $y = - \frac { \sqrt { 800 - 25 x ^ { 2 } } } { 4 }$

Question

Quizplus · Accepted Answer

To graph the ellipse, we need to solve the given equation for $y$. Starting with $\frac{x^2}{16} + \frac{(y-5)^2}{25} = 1$, we isolate $y-5$ and then solve for $y$, resulting in two equations: one for the positive square root and one for the negative. The correct transformations and simplifications lead to the equations in choice A, which correctly adjust for the center of the ellipse being shifted up by 5 units and account for the correct semi-major and semi-minor axes lengths.

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