Find the lengths of the major and minor axes for the ellipse. $\frac { x ^ { 2 } } { 13 } + \frac { y ^ { 2 } } { 49 } = 1$
A) major axis: $14$
, minor: $2 \sqrt { 13 }$
B) major axis: $7$
, minor: $2 \sqrt { 14 }$
C) major axis: $49$
, minor: $2 \sqrt { 13 }$
D) major axis: $14$
, minor: $14$
E) none of these

Question

Quizplus · Accepted Answer

The lengths of the major and minor axes for an ellipse given by the equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ are $2a$ and $2b$, respectively, where $a$ and $b$ are the semi-major and semi-minor axes lengths. In this case, $a^2 = 49$ and $b^2 = 13$, so $a = \sqrt{49} = 7$ and $b = \sqrt{13}$. Therefore, the lengths of the major and minor axes are $2a = 14$ and $2b = 2\sqrt{13}$, respectively.

Find the Lengths of the Major and Minor Axes for the Ellipse