How do you find the eccentricity, directrix, focus and classify

simsek6li

simsek6li

Answered question

2022-02-10

How do you find the eccentricity, directrix, focus and classify the conic section r=841.6sinθ?

Answer & Explanation

totemicccn

totemicccn

Beginner2022-02-11Added 10 answers

Eccentricity is e=0.4, directrix is y=5, focus is at pole (0, 0) and the conic is ellipse.
Explanation:
r=841.6sinθ, this is similar to standard equation,
r=ep1esinθe,p are eccentricity of conic and distance of directrix from the focus at pole. (-) sign indicates that the directrix is below the focus and parallel to the polar axis
r=841.6sinθ=8441.6sinθ4 or
r=841.6sinθe=0.4and ep=2or p=20.4 or
p=5;e<1 conic is ellipse and directrix is 5 units below the pole parallel to the polar axis. Rectangular conversion:
4r1.6rsinθ=8or 4x2+y21.6y=8.
Eccentricity is e=0.4, directrix is y=5, focus is at pole (0, 0) and the conic is ellipse.

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