Find the equation of an ellipse by eliminating the parameter of parametric equations

The video tutorial explains how to eliminate the parameter Theta from two given equations using the Pythagorean identity. The instructor demonstrates solving for sine and cosine of Theta, forming an equation with squared terms, and identifying the resulting shape as an ellipse rather than a circle. The tutorial concludes with a preview of the next chapter.

Explain the process of rewriting the equation to eliminate denominators.

What conclusion can be drawn about the shape of the graph based on the coefficients of X and Y?