Question

Number of points having distance $\sqrt{5}$ from the straight line $x-2y+1=0$ and a distance $\sqrt{13}$ from the line $2x+3y-1=0$, is/are?

• A. $1$
• B. $2$
• C. $4$
• D. $5$

Answer 1

Answer: (C)

$4$

Let the point be $(h,k)$.

Then, $\left|\frac{h-2k+1}{\sqrt{1^2+(-2{)}^2}}\right|=\sqrt{5}$
$\Rightarrow h-2k+1=\pm 5$ ...(i)

Also,

$\left|\frac{2h+3k-1}{\sqrt{2^2+3^2}}\right|=\pm 13$ ...(ii)

On solving Eqs. (i) and (ii), we get four points.

So, there are such $4$ points.