### Pedal Equation

**The (p , r) or Pedal Equation of Curve :-**

We have been acquainted with two types of equation of any curve ; one Cartesian Equation

**and the other the Polar Equation containing**

*(x,y)**. When the equation of any curve is given in terms of*

**(r,theta)***where*

**(p,r)***is the length of the perpendicular from the pole on the*

**p***and*

**tangent***is the radius vector , then that form of the curve is called the Pedal Equation .*

**r****Find the pedal equation of a curve from its polar form :-**

Let the polar equation of any curve be ,

*f(r,theta)=0 --------------------(1)*Let the coordinates of any point on the curve be

*and let the length of perpendicular from the pole on the tangent at*

**(r,theta)***be*

**(r,theta)***.*

**p**If

*be the angle between the tangent and the radius vector ,*

**phai**then we know that ,

**tan (phai) = r .d theta /dr ----------(2)**

**and p=r . sin(phai) ---------------(3)**Now , if we eliminate

*between the equations*

**theta***and*

**(1) , (2)***then we shall get an equation in terms of*

**(3)***and*

**p***and thus will be required an equation of the curve .*

**r**
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