Question

The coordinates of a point on the line $x+y+3=0$ whose distance from $x+2y+2=0$ is $\sqrt{5}$ is equal to

• A. $(9,6)$
• B. $(-9,6)$
• C. $(-9,-6)$
• D. none of these

Answer 1

The correct option is B $(-9,6)$

Let $P(x_1,y_1)$ be the required point on the line.
$\Rightarrow x_1+y_1+3=0$ ....(i)
Now, $d=\frac{|x_1+2y_1+2|}{\sqrt{5}}$
$\sqrt{5}=\frac{|x_1+2y_1+2|}{\sqrt{5}}$
$x_1+2y_1+2=\pm 5$
$\Rightarrow x_1+2y_1=3$ ....(ii)
and $\Rightarrow x_1+2y_1=-7$ ......(iii)
Solving (i) and (ii),we get
$x_1=-9,y_1=6$
Solving (i) and (iii),we get
$x_1=1,y_1=-4$
So, the points are (-9,6) and (1,-4)