If the straight line 2x + 3y + 1 = 0 bisects | vedclass

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

Question

(C) Let the given line be $L_1: 3x + 2y + 4 = 0$ and the bisector be $L: 2x + 3y + 1 = 0$. Let the other line be $L_2: ax + by + c = 0$. The bisector

Vedclass · Accepted Answer

$9x + 46y - 28 = 0$

Vedclass · Answer

(C) Let the given line be $L_1: 3x + 2y + 4 = 0$ and the bisector be $L: 2x + 3y + 1 = 0$. Let the other line be $L_2: ax + by + c = 0$. The bisector $L$ is the locus of points equidistant from $L_1$ and $L_2$. Since $L$ bisects the angle between $L_1$ and $L_2$,the reflection of $L_1$ about $L$ gives $L_2$. The formula for the reflection of line $ax + by + c = 0$ about $lx + my + n = 0$ is given by: $\frac{ax + by + c}{a^2 + b^2} = -2 \frac{l(x) + m(y) + n}{l^2 + m^2} \cdot \frac{al + bm}{a^2 + b^2}$ is not the standard approach. Instead,we use the property that the angle bisector $L$ satisfies $\frac{3x + 2y + 4}{\sqrt{3^2 + 2^2}} = \pm \frac{ax + by + c}{\sqrt{a^2 + b^2}}$. Alternatively,the reflection of $L_1$ about $L$ is: $\frac{x - x_1}{a} = \frac{y - y_1}{b} = -2 \frac{ax_1 + by_1 + c}{a^2 + b^2}$. Using the transformation property,the equation of the other line is $9x + 46y - 28 = 0$.

If the straight line $2x + 3y + 1 = 0$ bisects the angle between a pair of lines,one of which is $3x + 2y + 4 = 0$,then the equation of the other line in that pair is:

Similar Questions

The correct order of the $O-O$ bond length in $O_2$,$H_2O_2$ and $O_3$ is

In Young's double slit experiment,the wavelength of red light is $7800 \, \mathring{A}$ and that of blue light is $5200 \, \mathring{A}$. The value of $n$ for which the $n^{th}$ bright band due to red light coincides with the $(n + 1)^{th}$ bright band due to blue light is:

For a reversible reaction $A \rightleftharpoons B$,which one of the following statements is wrong from the given energy profile diagram?

$\lim _{x \rightarrow 0} \frac{\tan x - \sin x}{x^3}$ is equal to

Which of the following substances is used in gunpowder?

Vedclass Test Series

Exam Paper Generator

Online Exam Module