# 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}