Find the polar coordinates of the point(s) of intersection of the given curves for 0 $$0 \leq \theta

Question

Find the polar coordinates of the point(s) of intersection of the given curves for 0 $$0 \leq \theta < 2 \pi$$
-$$r = \frac { a \left( 1 - e ^ { 2 } \right) } { 1 + e \cos \theta }$$ Given that the polar equation r models the orbits of the planets, compare Earth's orbit relative to the sun with that of Pluto and describe the difference. For Earth, a = 1.00 and e = 0.017.
For Pluto, a = 39.4 and e = 0.249.
A) Earth's orbit closely approximates a circle with the sun positioned at its center. Pluto's orbit is more elliptical with the sun positioned on its long axis about 10 astronomical units away from
The center.
B) Earth circles the sun, but Pluto does not.
C) The orbits of Earth and Pluto are both circular, with the sun positioned at their centers, but the diameter of Pluto's orbit is about 40 times that of Earth.
D) Pluto's orbit closely approximates a circle with the sun positioned at its center. Earth's orbit is more elliptical with the sun positioned on its long axis about 10 astronomical units away from
The center.

Quizplus · Accepted Answer

The given polar equation is a form of Kepler's equation for the orbits of planets, where $a$ is the semi-major axis and $e$ is the eccentricity. Earth's orbit, with $e = 0.017$, is nearly circular, making the sun almost at the center. Pluto, with $e = 0.249$, has a more elliptical orbit, placing the sun off-center along the long axis.

Find the Polar Coordinates of the Point(s) of Intersection of the Given