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

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}.


(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}.

Finding the Polar Equivalent of an Equation for a Curve:

To transform an equation of a curve into its polar equivalent, we write the equation in terms of the variables {eq}r {/eq} and {eq}\theta {/eq} using the equations {eq}x = r \cos \theta {/eq} and {eq}y = r \cos \theta {/eq} and possibly even using trigonometric identities to simplify the resulting equation.

Answer and Explanation: 1

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We use the polar equivalents {eq}x = r \cos \theta {/eq} and {eq}y = r \sin \theta {/eq} which allows us to write

(a) $$\begin{align*} 9x + y &=...

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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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