Eliminate the parameter of a sideways parabola

The video tutorial discusses solving for T in equations, initially focusing on the X equation but noting its complexity due to multiple T terms. It suggests an alternative approach by solving for T in the Y equation, which simplifies the process. The tutorial then simplifies the equation for X and identifies the resulting curve as a horizontal parabola. It concludes with advice on when to solve for T in the X equation and when to use the Y equation.

How does flipping the X and Y axes affect the orientation of the graph?

What is the expected outcome when eliminating the parameter in the given equations?