Question

The perpendicular distance from the point $(2,-3)$ to a line which makes equal intercepts on the co-ordinate axis is $4$ units. Then the value of the intercept is

• A. $-1-2\sqrt{2}$
• B. $-1+2\sqrt{2}$
• C. $-1-3\sqrt{2}$
• D. $-1-4\sqrt{2}$

Answer 1

The correct option is D $-1-4\sqrt{2}$

The equation of the line which makes equal intercepts on the co-ordinate axis is given by
$x+y=c$
Perpendicular distance is,
$\frac{2-3-c}{\sqrt{1+1}}=4\Rightarrow -1-c=\pm 4\sqrt{2}\Rightarrow c=-1\pm 4\sqrt{2}$