Solve.
-The planets in a certain solar system have a path that is an ellipse, with Star A as one of the foci. Planet $X$ has a perihelion of 588.6 million miles and an aphelion of 631.8 miles. Find an equation for Planet X's orbit. Express your answer with $a$ and $b$ in millions of miles, rounded to the nearest tenth of a million.
A) $\frac{x^{2}}{610.2^{2}}+\frac{y^{2}}{609.8^{2}}=1$

B) $\frac{x^{2}}{609.2^{2}}+\frac{y^{2}}{610.8^{2}}=1$

C) $\frac{x^{2}}{610.8^{2}}+\frac{y^{2}}{609.2^{2}}=1$

D) $\frac{\mathrm{x}^{2}}{609.8^{2}}+\frac{\mathrm{y}^{2}}{610.2^{2}}=1$

Question

Solve.
-The planets in a certain solar system have a path that is an ellipse, with Star A as one of the foci. Planet $X$ has a perihelion of 588.6 million miles and an aphelion of 631.8 miles. Find an equation for Planet X's orbit. Express your answer with $a$ and $b$ in millions of miles, rounded to the nearest tenth of a million.
A) $\frac{x^{2}}{610.2^{2}}+\frac{y^{2}}{609.8^{2}}=1$

B) $\frac{x^{2}}{609.2^{2}}+\frac{y^{2}}{610.8^{2}}=1$

C) $\frac{x^{2}}{610.8^{2}}+\frac{y^{2}}{609.2^{2}}=1$

D) $\frac{\mathrm{x}^{2}}{609.8^{2}}+\frac{\mathrm{y}^{2}}{610.2^{2}}=1$

Quizplus · Accepted Answer

The semi-major axis $a$ is the average of the perihelion and aphelion distances: $a = \frac{588.6 + 631.8}{2} = 610.2$ million miles. The semi-minor axis $b$ is found using the formula $b = \sqrt{a^2 - c^2}$, where $c$ is the distance from the center to a focus. Since $c = \frac{631.8 - 588.6}{2} = 21.6$ million miles, $b = \sqrt{610.2^2 - 21.6^2} \approx 609.8$ million miles. Therefore, the equation is $\frac{x^{2}}{610.2^{2}}+\frac{y^{2}}{609.8^{2}}=1$.

Solve -The Planets in a Certain Solar System Have a Path

Solve
-The Planets in a Certain Solar System Have a Path