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