Question

Eliminate the parameter,t, in the parametric equation, x=6cos t, and y =3 sin t

Answer 1

X = 6 cos(t) 
y = 3 sin(t)

we can rewrite these equations as:

$\frac{x}{6}=cost(t) \\ \\ \frac{y}{3} =sin(t)$

Taking squares of both equations we get:

$( \frac{x}{6})^{2}=sin^{2} (t) \\ \\ ( \frac{y}{3})^{2}=cos^{2}(t)$

Adding both the equations, we get:

$\frac{ x^{2} }{36}+ \frac{ x^{2} }{9}=sin^{2}(t)+cos^{2}(t) \\ \\ \frac{ x^{2} }{36}+ \frac{ x^{2} }{9}=1$