Straight Line and Pair of Straight Lines 1 Question 10

10. If a straight line passing through the point $P(-3,4)$ is such that its intercepted portion between the coordinate axes is bisected at $P$, then its equation is

(2019 Main, 12 Jan II)

(a) $x-y+7=0$

(b) $4 x-3 y+24=0$

(c) $3 x-4 y+25=0$

(d) $4 x+3 y=0$

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Solution:

  1. Let the equation of required line having intercepts $a$ and $b$ with the axes is

Now, according to given information,

$P$ is the mid-point of $A B$

$\therefore \quad P=\frac{a}{2}, \frac{b}{2}=(-3,4)$

[given]

$$ \Rightarrow \quad(a, b)=(-6,8) $$

On putting the value of $a$ and $b$ in Eq. (i), we get

$$ \begin{aligned} \frac{x}{-6}+\frac{y}{8} & =1 \Rightarrow 8 x-6 y=-48 \\ \Rightarrow \quad 4 x-3 y+24 & =0 \end{aligned} $$



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