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  4. A line through P(3,5) is such that its intercept between the axes bisected at P . Its equation is

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Q. A line through $ P(3,5) $ is such that its intercept between the axes bisected at $ P $ . Its equation is

J & K CETJ & K CET 2017Straight Lines

Solution:

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Let the line $L$ has intercept of $AB$ between the axes
Since $AB$ is bisected at $P$
$\therefore \frac{a+0}{2}=3$
and $\frac{0+b}{2}=5$
$\Rightarrow a=6$ and $b=10$
$\therefore A \equiv\left(6,0\right)$
and $B=(0, 10)$
$\therefore $ Equation of line $L$ is given by
$\frac{x}{6}+\frac{y}{10}=1$
$\Rightarrow 5x+3y=30$