Answer:
Explanation: Consider the attached ellipse. Let the sun be at the right focus. Then perihelion is at right vertex on the x-axis and aphelion is at the left vertex on the x-axis.
The distances:
from perihelion to the sun in terms of ellipse is a-c;
from aphelion to the sun in terms of ellipse is a+c.
Then
Add these two equations:
and subtract first equation from the second:
Note that thus
The equation for the planet's orbit is