Eliminate the parameter t from the parametric equations x 2

Eliminate the parameter t from the parametric equations x - -2 sin t,y = 3 cos t, and find the corresponding rectangular equation.

Solution

Given Parametric equations x=-2Sin(t), y= 3Cos(t)

x=-2Sin(t)=> x/2=-Sin(t)---> 1

y=3Cos(t)=> y/3=Cos(t)---> 2

Squaring and Adding equations 1 and 2

X²/4 + Y²/9= Sin²(t) + Cos²(t) From Trigonometric identity Sin²(t) + Cos²(t)= 1

Therefore X²/4 + Y²/9=1

Required rectangular equation is X²/4 + Y²/9=1