Find a polar equation for the curve represented by the given Cartesian equation: a) 9x + y = 6 ...

Question:

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

a) {eq}9x + y = 6 {/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 = 5 {/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 Coordinates:

To convert from Cartesian to polar coordinates, we use the familiar relations below. We simply substitute the polar equivalent of the Cartesian coordinate(s) directly into the curve.

{eq}x = r \cos \theta \\ y = r \sin \theta \\ r^2 = x^2+y^2 \\ \tan \theta = \frac{y}{x} {/eq}

Answer and Explanation: 1

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Part A

We have

{eq}\begin{align*} 9x+y &= 6 \\ 9r\cos \theta + r\sin \theta &= 6 \\ r (9\cos \theta + \sin \theta) &= 6 \\ r &= \frac6{9\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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