Difficult ellipse Word Problem

Question

I have a difficult word problem involving conics and I don't even know where to begin

Pluto orbits the sun in an elliptical path the center of the sun is the focus of the ellipse. The eccentricity of the orbit is e = 0.249.  The length of the major axis is about 79.0 astronomical units.

I need to find the equation for pluto's orbit around the sun.

The problem also says I can assume that the major axis is horizontal.

Answer 1

Equation of ellipse: x^2/a^2+y^2/b^2=1, where a is the length of the semimajor axis, while b is that of the semiminor axis. b^2=a^2(1-e^2) where e=eccentricity. a=79AU; e=0.249, so b=sqrt(6241(1-0.062001))=76.51AU.

x^2/79^2+y^2/76.5^2=1 or x^2/6241+y^2/5854=1.