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}

Question

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 θ}

Answer 1

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

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}

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