# 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}