How to find the rectangular equation for the following parametric equation?

Question

x=4+2cos(x) y=-1+sin(x)

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Answer 1 · 2018-03-20T07:01:41

The equation is #(x-4)^2/4+(y+1)^2=1#

The parametric equations are

#x=4+2cosx#

#y=-1+sinx#

Therefore,

#cosx=(x-4)/2#

and

#sinx=y+1#

Apply the trigonometric identity

#cos^2x+sin^2x=1#

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

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

This is the equation of an ellipse

graph{(x-4)^2/4+(y+1)^2-1=0 [-1.64, 10.844, -3.41, 2.83]}