How do you combine the parametric equations into one equation relating y to x given x=4cost and y=9sint?

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Answer 1 · 2016-06-20T07:50:37

#x^2/16+y^2/81=1#

As #x=4cost# and #y=9sint#, hence

#cost=x/4# and #sint=y/9#

Squaring the two and adding

#cos^2t+sin^t=x^2/16+y^2/81#

or #x^2/16+y^2/81=1#

This is the equation of a vertical ellipse.

graph{x^2/16+y^2/81=1 [-20, 20, -10, 10]}