plotting – Find points on a ellipse and plot the graph

For $a=1.5$, find the four points at which the ellipse


where $a>0,, b>0$ and intersects the curve $a,b,pi=5$.

Give your answers as exact values. Produce a plot showing the initial curve and the ellipse, with a large orange dot at each of the four intersection points.

I am very new to use the Mathematica and this website ;] I don’t know which command I should use. I will appreciate any help..

BTW, this is my classwork question and I just want to figure it out.