Straight LineHardBloom L3
Question
The equation of the pair of bisectors of the angles between two straight lines is, $12x^{2} - 7xy - 12y^{2} = 0$. If the equation of one line is $2y - x = 0$ then the equation of the other line is:
Options
A.$41x - 38y = 0$
B.$11x + 2y = 0$
C.$38x + 41y = 0$
D.$11x - 2y = 0$
Solution
Sol. [Key Concept: Given the pair of angle bisectors and one line, the other line is the reflection of the first across a bisector.]
Image of point $(2,1)$ lying on $2y - x = 0$ w.r.t. $4x + 3y = 0$ is
$$\begin{matrix} & \frac{x - 2}{4} = \frac{y - 1}{3} = - 2\frac{8 + 3}{25} \\ \Rightarrow \ & \ (x,y) \equiv \left( - \frac{38}{25}, - \frac{41}{25} \right) \end{matrix}$$
$\therefore\ $ Other line passes through $(0,0)$ and $\left( - \frac{38}{25}, - \frac{41}{25} \right)$ and is given by
$$y = \frac{41}{38}x$$
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