Halley's Comet orbits the sun every 76 years. The comet travels in an elliptical path, with the sun at one of the foci. At the closest point, or perihelion, the distance of the comet to the sun is 8.8 x 10^7 km. At the furthest point, or aphelion, the distance of the comet from the sun is 5.3 x 10^9 km. Write an equation of the ellipse that models the path of Halley's Comet. Assume the sun is on the x-axis.

They don't give me the radius of the sun, so should I treat it as just a point?

I put the center at the origin. The closest distance will be "a" less "c". The other distance will be "c" plus "a". So I have:

8.8 x 10^7 = a - c

5.3 x 10^9 = a + c

Adding gives me 8.8 x 10^7 + 5.3 x 10^9 = 2a, so (8.8 + 530) x 10^7 = 2a, a = 269.4 x 10^7 = 2.694 x 10^9. Then c = 2.606 x 10^9. a^2 - c^2 = b^2, so b = 0.4664 x 10^9.

Am I doing this right?