Short Answer

Find a polar equation for the curve represented by the given Cartesian equation.
\({\rm{x y = 4}}\)

The curve's polar equation is

\({{\rm{r}}^{\rm{2}}}{\rm{ = 8csc2\theta }}\)

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The curve's polar equation.

\(\begin{aligned}{l}{\rm{x = rcos\theta ,}}\;\;\;{\rm{y = rsin\theta }}\\{\rm{xy = 4(rcos\theta )(rsin\theta ) = 4}}\\{{\rm{r}}^{\rm{2}}}{\rm{cos\theta sin\theta = 4}}\\{{\rm{r}}^{\rm{2}}}{\rm{ = }}\frac{{\rm{4}}}{{{\rm{cos\theta sin\theta }}}}\\{{\rm{r}}^{\rm{2}}}{\rm{ = }}\frac{{\rm{8}}}{{{\rm{sin2\theta }}}}\end{aligned}\)

Step 2: As a result, the curve's polar equation is.

It's important to understand that r is not the same as radius; it's simply a parameter that can take any actual value.

\({{\rm{r}}^{\rm{2}}}{\rm{ = 8csc2\theta }}\)

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Essential Calculus: Early Transcendentals

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Short Answer

Find a polar equation for the curve represented by the given Cartesian equation.
\({\rm{x y = 4}}\)

Step by Step Solution

Step 1: The curve's polar equation.

Step 2: As a result, the curve's polar equation is.

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Essential Calculus: Early Transcendentals

Answers without the blur.

Short Answer

Find a polar equation for the curve represented by the given Cartesian equation. \({\rm{x y = 4}}\)

Step by Step Solution

Step 1: The curve's polar equation.

Step 2: As a result, the curve's polar equation is.

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Find a polar equation for the curve represented by the given Cartesian equation.
\({\rm{x y = 4}}\)