**Definition of Polar Equation**

- An equation of a curve in terms of polar coordinates
*r*and*θ*is called a Polar Equation.

**More about Polar Equation**

- The number of petals in the graph of a polar equation
*r*=*a*sin*nθ*or*r*=*a*cos*nθ*is ‘*n*’, if*n*is odd, and ‘2*n*’, if*n*is even, where ‘*a*’ - If the polar equation is
*r*(-*θ*) =*r*(*θ*), then the curve is symmetrical about the horizontal axis. - If the polar equation is
*r*(*π*-*θ*) =*r*(*θ*), then the curve is symmetrical about the vertical axis.

**Example of Polar Equation**

*r*= 3sin 4*θ*and*r*= 2cos 5*θ*are polar equations as they are written in terms of*r*and*θ*.

**Solved Example on Polar Equation**

Convert the rectangular equation

y^{2}=x^{3}to polar equation.

Choices:

A. r = tan^{2}θsecθ

B. r = tan^{2}θ

C. r^{2}= tan^{2}θsecθ

D. r = cot^{2}θcosθ

Correct Answer: A

Solution:

Step 1:y=^{2}x^{3}[Rectangular equation.]

Step 2:(rsinθ)^{2}= (rcosθ)^{3}[Usey=rsinθandx=rcosθ]

Step 3:rsin^{2}^{2}θ=r^{3}cos^{3}θ

Step 4:sin^{2}θ/ cos^{3}θ=r^{3}/r^{2}

Step 5:r= tan^{2}θsecθ[Use trigonometric definitions.]

Step 6:So, the polar equation isr= tan^{2}θsecθ.

**Related Terms for Polar Equation**

- Coordinates
- Curve
- Equation
- Polar Form