Question

A line is drawn through a fixed point $(h,k)$ cutting the coordinate axes at P and Q respectively. The rectangle OPRQ is completed. Find the equation of locus of R.

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

Answer 1

Answer: (C)

Let the coordinates of $R(\alpha ,\beta )$. Since, OPRQ is a rectangle, therefore coordinates of $P$ and $Q$ are $(\alpha ,0)$ and $(0,\beta )$ respectively. Now, equation of line $PQ$ is
$\frac{x}{\alpha }+\frac{y}{\beta }=1$
Since, $(h,k)$ lies on this line
$\therefore \frac{h}{\alpha }+\frac{k}{\beta }=1$

Hence, locus of $R(\alpha ,\beta )$ is
$\frac{h}{x}+\frac{k}{y}=1$