Straight Lines
Angle bisectors of pair of straight lines
nta_pyq_2023_jan
Grade 11
Question:
The combined equation of the two lines $ax + by + c = 0$ and $a'x + b'y + c' = 0$ can be written as $(ax + by + c)(a'x + b'y + c') = 0$. The equation of the angle bisectors of the lines represented by the equation $2x^2 + xy - 3y^2 = 0$ is
3x^2 + 5xy + 2y^2 = 0
x^2 - y^2 + 10xy = 0
3x^2 + xy - 2y^2 = 0
x^2 - y^2 - 10xy = 0
Step-by-Step Solution
Key Concept: For the pair of lines $ax^2 + 2hxy + by^2 = 0$, the equation of angle bisectors is $\frac{x^2 - y^2}{a - b} = \frac{xy}{h}$.
$\frac{x^2-y^2}{5} = \frac{xy}{1/2} \Rightarrow x^2 - y^2 - 10xy = 0$.
Correct Answer: 4