Question

The coordinates of point(s) on $x+y+3=0,$ whose distance from $x+2y+2=0$ is $\sqrt{5}$ , is(are)

• A. $(9,6)$
• B. $(-9,6)$
• C. $(6,-9)$
• D. $(1,-4)$

Answer 1

Answer: (B), (D)

$(-9,6)$
$(1,-4)$

Let the required point be $(x_1,y_1)$ Since it lies on $x+y+3=0.$
$\therefore x_1+y_1+3=0$ ........(1)
Now length of the perpendicular from $(x_1,y_1)$ to $x+2y+2=0$ is $\sqrt{5}$
$\Rightarrow \left|\frac{x_1+2y_1+2}{\sqrt{1^2+2^2}}\right|=\sqrt{5}\Rightarrow x_1+2y_1+2=\pm 5$ ........(2)
On solving equations $\left(1\right)$ and $\left(2\right),$
we get $x_1=-9,y_1=6$ and $x_1=1,y_1=-4$
Hence the required points are $(-9,6),(1,-4)$