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Find a polar equation for the curve represented by the given Cartesian equation: a) 4x+4y=9 ...

Question:

Find a polar equation for the curve represented by the given Cartesian equation:

a) {eq}4x+4y=9 {/eq}

Write the answer in the form {eq}r=f(t) {/eq} where {eq}t {/eq} stands for {eq}\theta. {/eq}

Polar equation: {eq}r=\; \rule{20mm}{.5pt} {/eq}

b) {eq}x^2-y^2=4 {/eq}

Write the answer in the form {eq}r^2=f(t) {/eq} where {eq}t {/eq} stands for {eq}\theta {/eq}.

Polar equation: {eq}r^2=\; \rule{20mm}{.5pt} {/eq}

Polar Equation:

A function expressed in rectangular coordinates y=f(x) can be converted to polar coordinates

by accounting for transformation formulas from rectangular to polar coordinates

{eq}x= r \cos \theta \\ y= r \sin \theta {/eq}

Answer and Explanation: 1

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By accounting for transformation formulas from rectangular to polar coordinates

{eq}x= r \cos \theta \\ y= r \sin \theta {/eq}

the following...

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Cylindrical & Spherical Coordinates: Definition, Equations & Examples

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Chapter 13 / Lesson 10
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Learn how to convert between Cartesian, cylindrical and spherical coordinates. Discover the utility of representing points in cylindrical and spherical coordinates.


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