Question

Convert the rectangular equation to polar formAssume a> 02x +3y -5 =0

Answer 1

Given,

The equation is 2x +3y -5 =0

Taking the equation as 2x + 3y =5

Taking,

$\begin{gathered} x\text{ = r cos }\theta \\ y=r\text{ sin }\theta \end{gathered}$

Subsituting the value of x and y in the given equation then,

$\begin{gathered} 2(r\text{ cos }\theta)+3(\text{ r sin }\theta)=5 \\ r(2\text{ cos }\theta+3\sin \theta)=5_{} \\ r=\frac{5}{2\text{ cos }\theta+3\sin \theta} \end{gathered}$

Hence, this is the required polar equation.