Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$$
A) $y = \sqrt { \frac { 245 - x ^ { 2 } } { 7 } }$ and $y = - \sqrt { \frac { 175 - x ^ { 2 } } { 7 } }$

B) $y = \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 7 }$ and $y = - \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 7 }$

C) $y = \sqrt { \frac { 175 - x ^ { 2 } } { 5 } }$ and $y = - \sqrt { \frac { 175 - x ^ { 2 } } { 5 } }$

D) $y = \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 49 }$ and $y = - \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 49 }$

Question

Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$$
A) $y = \sqrt { \frac { 245 - x ^ { 2 } } { 7 } }$ and $y = - \sqrt { \frac { 175 - x ^ { 2 } } { 7 } }$

B) $y = \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 7 }$ and $y = - \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 7 }$

C) $y = \sqrt { \frac { 175 - x ^ { 2 } } { 5 } }$ and $y = - \sqrt { \frac { 175 - x ^ { 2 } } { 5 } }$

D) $y = \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 49 }$ and $y = - \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 49 }$

Quizplus · Accepted Answer

To graph the ellipse $\frac{x^2}{49} + \frac{y^2}{25} = 1$, we solve for $y$ to get two equations, one for the upper half and one for the lower half of the ellipse. Multiplying both sides by 25 gives $y^2 = 25(1 - \frac{x^2}{49})$, which simplifies to $y^2 = 25 - \frac{25x^2}{49}$. Taking the square root of both sides gives $y = \pm\sqrt{25 - \frac{25x^2}{49}}$, which simplifies to $y = \pm\frac{5\sqrt{49 - x^2}}{7}$, matching choice B.

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