CAT Exam Model Paper 1 with solutions for free online practice

(a) Equation of any line L perpendicular to
5x − y = 1 is x + 5y = k ...(i)
Where k is an arbitrary constant.
If this line cuts x-axis at A and y-axis at B, then for A, y = 0 and from (i) x = k i.e., A is the point (k, 0). For B, x = 0 and from (i) y = $\frac{\mathit{k}}{5}$i.e., B is the point $\left(0,\frac{\mathit{k}}{5}\right)$
∴ Area of the given ∆OAB = $=\frac{1}{2}\left({\mathit{x}}_1{\mathit{y}}_2-{\mathit{x}}_2{\mathit{y}}_1\right)$
$=\frac{1}{2}\left(\frac{{\mathit{k}}^2}{5}-0\right)=\frac{{\mathit{k}}^2}{10}$
But according to the given condition, $\frac{{\mathit{k}}^2}{10}=5$ or ${\mathit{k}}^2$= 50
∴ k = $\pm 5\sqrt{2}$
Hence, from (i), the required equation of the line is
x + 5y = $5\sqrt{2}$
or x + 5y = $-5\sqrt{2}$