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

Question

Prove that the product of the lengths of perpendiculars drawn from the points and to the line , is b 2

Philoid · Accepted Answer

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

At point B, m= and n= ,

D₂

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

D₁D₂

(In the numerator we have and )

D₁D₂

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