Find the eccentricity of the ellipse.
-$$25 x ^ { 2 } + 64 y ^ { 2 } = 1600$$
A) $\frac { \sqrt { 39 } } { 8 }$
B) $\frac { 39 } { 8 }$
C) $\frac { \sqrt { 89 } } { 8 }$
D) $\frac { \sqrt { 39 } } { 5 }$

Question

Quizplus · Accepted Answer

We first need to get the equation into standard form: 
$$\frac{x^2}{\left(\frac{8}{5}\right)^2}+\frac{y^2}{\left(\frac{5}{8}\right)^2}=1$$
Then, we can use the formula for eccentricity of an ellipse:
$$e=\sqrt{1-\left(\frac{b}{a}\right)^2}=\sqrt{1-\left(\frac{5}{8}\right)^2}=\frac{\sqrt{39}}{8}$$
Therefore, the best choice is A.

Find the Eccentricity of the Ellipse 25x2+64y2=160025 x ^ { 2 } + 64 y ^ { 2 } = 160025x2+64y2=1600

Find the Eccentricity of the Ellipse $25 x ^ { 2 } + 64 y ^ { 2 } = 1600$