Question

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

• A. $5x+3y=30$
• B. $3x+5y=30$
• C. $x+5y=30$
• D. $5x+y=30$

Answer 1

Answer: (A)

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
$\frac{x}{6}+\frac{y}{10}=1$
$\Rightarrow 5x+3y=30$