If the lengths of the perpendiculars drawn fr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the lines be $L_1: 2x + 3y + 4 = 0$ and $L_2: 3x - 2y + 4 = 0$.The length of the perpendicular from $(a, b)$ to $L_1$ is $d_1 = \frac{|2a + 3b

Vedclass · Accepted Answer

$x - 5y = 0$ or $5x + y + 8 = 0$

Vedclass · Answer

(C) Let the lines be $L_1: 2x + 3y + 4 = 0$ and $L_2: 3x - 2y + 4 = 0$.The length of the perpendicular from $(a, b)$ to $L_1$ is $d_1 = \frac{|2a + 3b + 4|}{\sqrt{2^2 + 3^2}} = \frac{|2a + 3b + 4|}{\sqrt{13}}$.The length of the perpendicular from $(a, b)$ to $L_2$ is $d_2 = \frac{|3a - 2b + 4|}{\sqrt{3^2 + (-2)^2}} = \frac{|3a - 2b + 4|}{\sqrt{13}}$.Given $d_1 = d_2$,we have $|2a + 3b + 4| = |3a - 2b + 4|$.This implies $2a + 3b + 4 = 3a - 2b + 4$ or $2a + 3b + 4 = -(3a - 2b + 4)$.Case $1$: $2a + 3b + 4 = 3a - 2b + 4 \Rightarrow a - 5b = 0$.Case $2$: $2a + 3b + 4 = -3a + 2b - 4 \Rightarrow 5a + b + 8 = 0$.Thus,the locus of $(a, b)$ is $x - 5y = 0$ or $5x + y + 8 = 0$.

If the lengths of the perpendiculars drawn from a point $(a, b)$ to the lines $2x + 3y + 4 = 0$ and $3x - 2y + 4 = 0$ are equal,then the point $(a, b)$ lies on the line

Similar Questions

Statement $-I$: Two lines which pass through a given fixed point and are equally inclined to two other lines passing through the same point,are always perpendicular to each other.
Statement $-II$: Angle bisectors of two intersecting lines are always perpendicular to each other.

The equal sides of an isosceles triangle are given by the equations $7x-y+3=0$ and $x+y-3=0$. If the slope $m$ of the third side is an integer,then $m=$

Let distinct lines $L_1$ and $L_2$ belong to the family of lines $(x - 2y - 3) + \lambda (x + 3y + 2) = 0$. If $B_1$ is the angle bisector of $L_1$ and $L_2$ which passes through the point $A(2, 3)$,then the equation of the other bisector of $L_1$ and $L_2$ is ($\lambda$ is a parameter).

The straight line $x+y+1=0$ bisects an angle between the pair of lines of which one is $2x+3y-4=0$. Then,the equation of the other line is

Let $P \equiv (-1, 0)$,$Q \equiv (0, 0)$,and $R = (3, 3\sqrt{3})$ be three points. The equation of the bisector of the angle $PQR$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module