Find the equation of the pair of lines perpendicular to the lines pair represented by the equation ax^2-2hxy+by^2=0 and passing through the origin.

The equation of the pair of lines perpendicular to the lines given equation is .

Solution:

Given equation is .

Let and be the slopes of the given lines.

Sum of the roots =

               – – – – – (1)

Product of the roots =

                    – – – – – (2)

The required lines are perpendicular to these lines.

Slopes of the required lines are

Required lines also passes through the origin,

therefore their y-intercepts are 0.

Hence their equations are:

Do cross multiplication, we get

Add x on both sides of the equation, we get

Therefore, the joint equation of the line is

Substitute (1) and (2), we get

To make the denominator same, multiply and divide first term by b.

Do cross multiplication, we get

Hence equation of the pair of lines perpendicular to the lines given equation is .