Answered: "Can it be shown that gives a conic..." - Plainmath

Joey Rodgers

Answered question

2022-03-18

Can it be shown that gives a conic section?

r^{2} = \frac{1}{1 - ε \cos (2 θ)}

Answer & Explanation

PCCNQN4XKhjx

Beginner2022-03-19Added 8 answers

Step 1
Rewrite it as

r^{2} (1 - ϵ \cos (2 θ))

= 1 \Leftrightarrow r^{2} (1 - ϵ (\cos^{2} θ - \sin^{2} θ)) = 1

and then expand. We have

r^{2} = x^{2} + y^{2}, r^{2} \cos^{2} θ = x^{2}

and

r^{2} \sin^{2} θ = y^{2}

so we get the traditional equation of an ellipse or a hyperbola.

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