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:


`(x)/(6)=cost(t) \\ \\ (y)/(3) =sin(t)`

Taking squares of both equations we get:


`( (x)/(6))^(2)=sin^(2) (t) \\ \\ ( (y)/(3))^(2)=cos^(2)(t)`

Adding both the equations, we get:


`( x^(2) )/(36)+ ( x^(2) )/(9)=sin^(2)(t)+cos^(2)(t) \\ \\ ( x^(2) )/(36)+ ( x^(2) )/(9)=1`