Question

The number of lines which pass through point $(2,-3)$ and are at a distance $8$ from point $(-1,2)$ is

• A. $\infty$
• B. $4$
• C. $2$
• D. $0$

Answer 1

The correct option is D $0$

The distance from the point $(-1,2)$ of the line which passes through $(2,-3)$
$=\sqrt{{(2+1)}^2+{(-3-2)}^2}$
$=\sqrt{9+25}=\sqrt{34}<8$
Given that the distance between the point $(-1,2)$ and the line is $8$
But the maximum distance of the line passing through $(2,-3)$ from $(-1,2)$ is $\sqrt{34}$. So, there is no such line possible.