Question

A line is drawn through the point $(1,2)$ to meet the coordinate axes at $P$ and $Q$ such that it form a triangle $OPQ$, where $O$ is least, then the slope and the line $PQ$ is

• A. $-2$
• B. $-1/2$
• C. $-1/4$
• D. $-4$

Answer 1

The correct option is A $-2$

Equation of line with x- intercept 'a' and

y- intercept 'b' is

$\frac{x}{a}+\frac{y}{b}=1$

$OP=a,$ $OD=b$

passes through (1,2)

$\frac{1}{a}+\frac{2}{b}=1$

$b=\frac{2a}{a-1}$

$A=\frac{1}{2}\times b\times a=\frac{a^2}{a-1}$

To minimize the area $\frac{dA}{da}=0$

$\frac{dA}{da}=\frac{a^2-2a}{(a-1{)}^2}=0$

$a=0,2$

At a=0, Area = 0 (Not possible)

$b=\frac{2a}{a-1}=4$

slope = $\frac{-b}{a}=\frac{-4}{2}=-2$