Provide an appropriate response.
-$$\frac { x ^ { 2 } } { 5476 } + \frac { y ^ { 2 } } { 5184 } = 1$$ where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)
A) 1.056
B) 0.231
C) 0.947
D) 3.946

Question

Quizplus · Accepted Answer

The eccentricity of an ellipse is given by $$e = \sqrt{1 - \frac{b^2}{a^2}}$$, where $a$ and $b$ are the semi-major and semi-minor axes, respectively. In the given equation, $\frac{x^2}{5476} + \frac{y^2}{5184} = 1$, we can identify $a^2 = 5476$ and $b^2 = 5184$. Thus, $$e = \sqrt{1 - \frac{5184}{5476}} = \sqrt{1 - \frac{5184}{5476}} = \sqrt{1 - 0.946} = \sqrt{0.054} \approx 0.231$$.

Provide an Appropriate Response x25476+y25184=1\frac { x ^ { 2 } } { 5476 } + \frac { y ^ { 2 } } { 5184 } = 15476x2​+5184y2​=1

Provide an Appropriate Response $\frac { x ^ { 2 } } { 5476 } + \frac { y ^ { 2 } } { 5184 } = 1$