Find the rectangular equation and curve represented by the p

Find the rectangular equation and curve represented by the parametric equations x = 1 + cos t and y = 2 sin t

Solution

x = 1 + cos t

cos t = (x-1)

y = 2 sin t

sin t = (y/2)

sin^2 t + cos^2 t =1

(x-1)^2 + (y/2)^2 = 1

4(x-1)^2 + y^2 = 4

This curve represents ellipse with (1,0) origin.