Find an equation equivalent to x^2-y^2=4 in polar coordinates.

Abril Huynh

Abril Huynh

Answered question

2023-03-26

Find an equation equivalent to x2-y2=4 in polar coordinates.

Answer & Explanation

unnlattpdui

unnlattpdui

Beginner2023-03-27Added 5 answers

Explanation to correct answer:
How to determine the polar coordinates:
We have,
x2-y2=4
The polar coordinates can be discovered using,
Substitute x=rcosθ and y=rsin(θ)
rcosθ2-rsinθ2=4r2cos2θ-r2sin2θ=4r2cos2θ-sin2θ=4r2cos2θ-1-cos2θ=4sin2θ=1-cos2θr2cos2θ-1+cos2θ=4r22cos2θ-1=4r2=42cos2θ-1r=22cos2θ-1
substitute r=22cos2θ-1
x=2cosθ2cos2θ-1
y=2sin(θ)2cos2θ-1
Therefore, the polar coordinates are 2cosθ2cos2θ-1,2sin(θ)2cos2θ-1.

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