Polar equations for conic sections Graph the following conic sections, labeling vertices, foci, directrices, and asymptotes (if they exist). Give the eccentricity of the curve. Use a graphing utility to check your work. r= frac{10}{5 + 2 cos theta}

FobelloE 2021-03-07 Answered
Polar equations for conic sections Graph the following conic sections, labeling vertices, foci, directrices, and asymptotes (if they exist). Give the eccentricity of the curve. Use a graphing utility to check your work. r= 105 + 2 cosθ
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Liyana Mansell
Answered 2021-03-08 Author has 97 answers

Step 1 GIven polar equation is: r= 105 + 2 cosθ The graph of the given polar equation is: image Step 2 Therefore the given polar equation represents an ellipse with major axis as the x-axis, center at (1, 0).
r= 10(5 + 2 cosθ}
r= 2[1 + (25) cosθ]
Eccentricity e= 25 < 1 Therefore the given equation represents an ellipse. Now we get, 2=ep
2= (25)p
p=5 The directrix is y=5.

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