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

What is the concentration of nitrate ions $(NO_3^-)$ if equal volumes of $0.1 \ M \ AgNO_3$ and $0.1 \ M \ NaCl$ are mixed together (in $M$)?

See the diagram. The area of each plate is $2.0\ m^2$ and $d = 2 \times 10^{-3}\ m$. $A$ charge of $8.85 \times 10^{-8}\ C$ is given to plate $Q$. Then the potential of $Q$ becomes......$V$.

In which stage does the condensation of chromosomes reach its maximum level?

What is the mycelium composed of?

If the normal to the curve $y^2 = 5x - 1$ at the point $(1, -2)$ is of the form $ax - 5y + b = 0$,then $a$ and $b$ are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module