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Found in: Page 535

### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

# Write a polar equation of a conic with the focus at the origin and the given data. Parabola, vertex $${\rm{(4,3}}\pi {\rm{/2)}}$$

Polar equation of a conic with the focus at the origin and the parabola, vertex $$\left( {{\rm{4,}}\frac{{{\rm{3}}\pi }}{{\rm{2}}}} \right)$$.

See the step by step solution

## Step 1: Conic sections are represented by polar equation.

Parabola with vertex $$\left( {{\rm{4,}}\frac{{{\rm{3}}\pi }}{{\rm{2}}}} \right)$$.

\begin{aligned}{l}{\rm{r = }}\frac{{{\rm{ed}}}}{{{\rm{1 \pm ecos\theta }}}},\;\;\\{\rm{r = }}\frac{{{\rm{ed}}}}{{{\rm{1 \pm esin\theta }}}}\end{aligned}

## Step 2: Polar equation.

$$e = 1$$

Pole and vertex $$\left( {{\rm{4,}}\frac{{{\rm{3}}\pi }}{{\rm{2}}}} \right)$$

Vertex is at the same distance from the foci as from the Directrix $${\rm{d = 2 \times 4 = 8}}$$

Polar Equation is,

\begin{aligned}{c}{\rm{r = }}\frac{{{\rm{ed}}}}{{{\rm{1 - esin\theta }}}}\\{\rm{ = }}\frac{{\rm{8}}}{{{\rm{1 - sin\theta }}}}\end{aligned}

## Step 3: Polar equation of a conic with the focus at the origin is.

$${\rm{ = }}\frac{{\rm{8}}}{{{\rm{1 - sin\theta }}}}$$