The orbit of Mars around the sun is an ellipse with equation $$\frac { x ^ { 2 } } { 6241 } + \frac { y ^ { 2 } } { 5184 } = 1$$ where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)
A) 0.831
B) 1.204
C) 13.380
D) 0.412

Question

Quizplus · Accepted Answer

The eccentricity of an ellipse is given by the formula $e = \sqrt{1 - \frac{b^2}{a^2}}$, where $a$ and $b$ are the semi-major and semi-minor axes, respectively. In the given equation, $a^2 = 6241$ and $b^2 = 5184$, so $a = \sqrt{6241}$ and $b = \sqrt{5184}$. Thus, $e = \sqrt{1 - \frac{5184}{6241}} = \sqrt{1 - \frac{5184}{6241}} = \sqrt{1 - 0.831} = \sqrt{0.169} \approx 0.412$.

The Orbit of Mars Around the Sun Is an Ellipse x26241+y25184=1\frac { x ^ { 2 } } { 6241 } + \frac { y ^ { 2 } } { 5184 } = 16241x2​+5184y2​=1

The Orbit of Mars Around the Sun Is an Ellipse $\frac { x ^ { 2 } } { 6241 } + \frac { y ^ { 2 } } { 5184 } = 1$