Straight Lines
Angular Bisector — Finding Coefficients
nta_pyq_2023_apr
Grade 11
Question:
If $l_1:\ 3y-2x=3$ is the angular bisector of $l_2:\ x-y+1=0$ and $l_3:\ \alpha x+\beta y+17=0$, then $\alpha^2+\beta^2-\alpha-\beta$ is equal to ............
Step-by-Step Solution
Key Concept: The bisector of $l_2$ and $l_3$ passes through their intersection and makes equal angles. Use the property: bisector equation from $l_2$ and $l_3$ must give $l_1$.
$\alpha^2+\beta^2-\alpha-\beta=348$.
Correct Answer: 348