Question

Locus of the mid points of the intercepts between the coordinate axes by the lines passing through $(a,0)$ does not intersect

• A. $x-$axis
• B. $y-$axis
• C. $y=x$
• D. $y=a$

Answer 1

The correct option is B $y-$axis

Let the intercepts of the line are $p\text{\&}q.$
Thus it's equation is given by, $\frac{x}{p}+\frac{y}{q}=1$
Given line also passes through $(a,0)$, $\Rightarrow p=a$
So, the coordinates on the axes are $(a,0),(0,q)$.
Let mid point of this segment be $(h,k)$
$\therefore h=\frac{a}{2},k=\frac{q}{2}$
So, $y=\frac{q}{2}$,
Since $a$ is given, so $x$-coordinated is fixed.