Question

The straight lines represented by $(y-mx{)}^2=a^2(1+m^2)$ and $(y-nx{)}^2=a^2(1+n^2)$ form a

• A. rectangle
• B. rhombus
• C. trapezium
• D. none of these

Answer 1

The correct option is B rhombus

$(y-mx{)}^2=a^2(1+m^2)$
$y-mx=\pm a\sqrt{1+m^2}$
$\frac{y}{|a\sqrt{1+m^2}|}-\frac{x}{|\frac{a\sqrt{1+m^2}}{m}|}=1$ --------(i)
Similarly
$(y-nx{)}^2=a^2(1+n^2)$
$y-nx=\pm a\sqrt{1+n^2}$
$\frac{y}{|a\sqrt{1+n^2}|}-\frac{x}{|\frac{a\sqrt{1+n^2}}{n}|}=1$ --------(ii)
From the intercept form of i and ii we get to know that the following four lines create a rhombus.