CUET PG 2026 — Mathematics PYQ

Solution

To find the equation of the pair of angle bisectors, we use the standard formula for a homogeneous second-degree equation.

1. General Form:

A pair of lines passing through the origin is represented by:

2. Identifying Coefficients:

From the given equation $x^2-4xy-5y^2=0$:

• $a=1$

• $2h=-4⟹h=-2$

• $b=-5$

3. Formula for Pair of Angle Bisectors:

The joint equation of the bisectors of the angles between the lines is:

4. Substituting the Values:

5. Simplifying the Equation:

Multiply both sides by $6$:

Rearranging the terms to one side:

Final Answer:

The correct option is (b) $x^2+3xy-y^2=0$.