Question

A variable line through the point $(a,b)$ cuts the axes of reference at $A$ and $B$ respectively. The lines through $A$ and $B$ parallel to the $y-$axis and the $x-$axis respectively meet at $P.$ Then the locus of $P$ has the equation

• A. $\frac{x}{a}+\frac{y}{b}=1$
• B. $\frac{x}{b}+\frac{y}{a}=1$
• C. $\frac{a}{x}+\frac{b}{y}=1$
• D. $\frac{b}{x}+\frac{a}{y}=1$

Answer 1

The correct option is C $\frac{a}{x}+\frac{b}{y}=1$

Line make $A$ and $B$ intercept on $x-$axis and $y-$axis on coordinate axis
The equation of line is
$\frac{x}{A}+\frac{y}{B}=1$
Where coordinate of $P$ are $(A,B)$
As point $(a,b)$ lies on line it will satisfy the equation
$\frac{a}{A}+\frac{b}{B}=1$
Hence replacing $A$ by $x$ and $B$ by $y$ we get the required equation of locus
$\frac{a}{x}+\frac{b}{y}=1$