How do you find the Cartesian equation from given parametric equations <mstyle displaystyle="tru

Scolfaro2y

Scolfaro2y

Answered question

2022-05-29

How do you find the Cartesian equation from given parametric equations x = 2 t 1 + t 4 and y = 2 t 3 1 + t 4 ?

Answer & Explanation

Austin Solis

Austin Solis

Beginner2022-05-30Added 12 answers

Step 1
We have
x y = 4 t 4 ( 1 + t 4 ) 2
Solving for t 4 we have
t 4 = 2 - x y ± 2 1 - x y x y
or
t = ± 2 - x y ± 2 1 - x y x y 4
now substituting into the x equation we have
x y ( 2 - x y + 2 1 - x y ) = x 4 which is a curve foil.
The curve is a rotated Bernoulli lemniscate.

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