Straight Lines
Straight Line
star_batch_jee_advanced_2025
Grade 11
Question:
Let $L_1: 3x + 4y = 1$ and $L_2: 5x - 12y + 2 = 0$ be two given lines. Let image of every point on $L_1$ with respect to a line $L$ lies on $L_2$ then possible equation of $L$ can be:
$14x + 112y - 23 = 0$
$64x - 8y - 3 = 0$
$11x - 4y = 0$
$52y - 45x = 7$
Step-by-Step Solution
Key Concept: The angle bisector of two lines is found by equating the perpendicular distances from a point on the bisector to both lines.
Line $L$ must be the angle bisector of lines $L_1$ and $L_2$. Setting the angle bisector equation: $\frac{3x + 4y - 1}{5} = \pm\frac{5x - 12y + 2}{13}$. Taking the positive sign gives $14x + 112y - 23 = 0$ and the negative sign gives $64x - 8y - 3 = 0$. Both equations represent the two angle bisectors.
Correct Answer: 1,2