Find a polar equation for the curve represented by the given Cartesian equation: a. 5x-3y=7....

Question:

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

a. {eq}5x-3y=7 {/eq}. Write the answer in the form {eq}r=f(t) {/eq}, where {eq}t {/eq} stands for {eq}\theta {/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 Coordinates:

There are many situations where a rectangular coordinate system is undesirable. For those situations where we are dealing with circles and/or circular regions, it is most convenient to use polar coordinates. Recall the following relations:

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

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

{eq}r^2 = x^2+y^2 {/eq}

{eq}\theta = \tan^{-1} \frac{y}{x} {/eq}

{eq}dA = r\ dr\ d\theta {/eq}

Answer and Explanation: 1

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Part A

We just plug in the equivalent polar representations of {eq}x {/eq} and {eq}y {/eq} to get

{eq}\begin{align*} 5x - 3y &= 7 \\ 5(r \cos...

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Graphing Functions in Polar Coordinates: Process & Examples

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Chapter 24 / Lesson 1
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Learn how to graph polar equations and plot polar coordinates. See examples of graphing polar equations. Transform polar to rectangular coordinates and vice versa.


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