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

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(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

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$9x + 46y - 28 = 0$

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(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:

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