Show that the cartesian equation of the curve that has the parameter 𝒙=𝟐+𝟑𝒄𝒐𝒔𝟐𝜽 and 𝒚=𝟒+𝟑𝒔𝒊𝒏𝟐𝜽 is 𝒙𝟐+𝒚𝟐−𝟒𝒙−𝟖𝒚+𝟏𝟏=𝟎.

Answer 1

cosθ = (x-2)/3
sinθ = (y-4)/3
since sin^2θ + cos^2θ = 1,
(x-2)^2/9 + (y-4)^2/9 = 1
Now just expand that out to get your x-y equation