# Thread: Polar Equation

1. ## Polar Equation

A curve with polar equation:

r= 44 / 4sinθ + 29cosθ

represents a line. This line has a Cartesian equation of the form
y = mx + b ,where m and b are constants. Give the formula
for y in terms of x. For example, if the line had equation
y = 2x+3 then the answer would be 2*x + 3 .

Please help!

2. Remember that: $\displaystyle x=r\cdot{\cos(\theta)}$, $\displaystyle y=r\cdot{\sin(\theta)}$ and $\displaystyle x^2+y^2=r^2$

3. Originally Posted by Del
A curve with polar equation:

r= 44 / 4sinθ + 29cosθ

represents a line. This line has a Cartesian equation of the form
y = mx + b ,where m and b are constants. Give the formula
for y in terms of x. For example, if the line had equation
y = 2x+3 then the answer would be 2*x + 3 .

Please help!
I assume you mean this

$\displaystyle r=\frac{44}{4\sin(\theta)+19 \cos(\theta)} \iff r(4\sin(\theta)+19 \cos(\theta))=44 =$

$\displaystyle 4\underbrace{r\sin(\theta)}_{y} + 19 \underbrace{r\cos(\theta)}_{x} =44 \iff 4y+19x=44$

So $\displaystyle y=-\frac{19}{4}x+11$