Prove that the product of the lengths of perpendiculars drawn from the points

and to the line , is b²

Given: Point , and line

To Prove: The product of the lengths of perpendiculars drawn from the points

and to the line , is b²

Formula used:

We know that the length of the perpendicular from (m,n) to the line ax + by + c = 0 is given by,

D

The equation of the line is

At point A, m= and n= ,

D₁

D₁

At point B, m= and n= ,

D₂

D₂

Product of the lengths of perpendiculars drawn from the points A and B is D₁D₂

D₁D₂

(In the numerator we have and )

D₁D₂

D₁D₂

D₁D₂

Product of the lengths of perpendiculars drawn from the points A and B is