According to Kepler’s Laws, planets have elliptical orbits, with the sun at one of the foci. The farthest Pluto gets from the sun is 7.4 billion kilometers. The closest it gets to the sun is 4.4 billion kilometers. Find the equation for Pluto’s orbit.

My work:

Using the perihelion, a - c = 4.4 billion km

Using the aphelion, a + c = 7.4 billion km

Adding 7.4 billion km + 4.4 billion km, I have 2a = 11.8 billion km

Dividing by 2, a = 5.9 billion km

b^2 = a^2 - c^2

= ((59 x 10^9)^2) - (15 x 10^9)^2 = 3.256 x 10^21

Equation of orbit = ((x^2)/(4.481 x 10^21)) + ((y^2)/(3.256 x 10^21)) = 1

Correct? Thanks in advance.