Question

From a point $P$, perpendiculars $PM,PN$ are drawn to $x$ and $y$ axes respectively. If $MN$ passes through fixed point $(a,b)$, locus of $P$, is

• A. $xy=ax+by$
• B. $xy=ab$
• C. $xy=bx+ay$
• D. $x+y=xy$

Answer 1

The correct option is C $xy=bx+ay$

$\left|\begin{array}{ccc}0& k& 1\\ a& b& 1\\ h& 0& 1\end{array}\right|=0(\because (o,k),(a,b),(h,o\left)arecollinear\right)$
$-k(a-h)+1(0-bh)=0$
$kh=bh+ak$
$xy=bx+ay$