Best solutions to - "Find an equation equivalent to x2-y2=4 in polar..."

Abril Huynh

Answered question

2023-03-26

Find an equation equivalent to

x^{2} - y^{2} = 4

in polar coordinates.

unnlattpdui

Beginner2023-03-27Added 5 answers

Explanation to correct answer:
How to determine the polar coordinates:
We have,

x^{2} - y^{2} = 4

The polar coordinates can be discovered using,
Substitute

x = r \cos (θ)

and

y = r \sin (θ)

{(r \cos (θ))}^{2} - {(r \sin (θ))}^{2} = 4 \Rightarrow r^{2} \cos^{2} (θ) - r^{2} \sin^{2} (θ) = 4 \Rightarrow r^{2} (\cos^{2} (θ) - \sin^{2} (θ)) = 4 \Rightarrow r^{2} (\cos^{2} (θ) - (1 - \cos^{2} (θ))) = 4 (∵ \sin^{2} (θ) = 1 - \cos^{2} (θ)) \Rightarrow r^{2} (\cos^{2} (θ) - 1 + \cos^{2} (θ)) = 4 \Rightarrow r^{2} (2 \cos^{2} (θ) - 1) = 4 \Rightarrow r^{2} = \frac{4}{2 \cos^{2} (θ) - 1} \Rightarrow r = \frac{2}{2}

substitute

r = \frac{2}{2}

x = \frac{2 \cos (θ)}{2}

y = \frac{2 \sin (θ)}{2}

Therefore, the polar coordinates are

(\frac{2 \cos (θ)}{2}, \frac{2 \sin (θ)}{2})

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