A closed curve in the (x,y) -plane is represented by

Aman Wyatt

Aman Wyatt

Answered question

2022-03-03

A closed curve in the (x,y) -plane is represented by the functions
x(θ)=12(cosθ+2(sinθ))
y(θ)=12(cosθ+2(sinθ))

Answer & Explanation

Goodwin2ug

Goodwin2ug

Beginner2022-03-04Added 6 answers

Clearly
1) 2x=cos(θ)+2sin(θ)
2) 2y=cos(θ)+2sin(θ)
Thus by 1)+2) we get,
2x+2y=22sin(θ)
So
x+y2=sin(θ)
Thus by 1)-2) we get,
2x2y=2cos(θ)
So
xy=cos(θ)
Now clearly
sin2(θ)+cos2(θ)=(x+y2)2+(xy)2=1
3x22xy+3y2=2

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