Question

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

• A. infinite
• B. 4
• C. 2
• D. 0

Answer 1

Answer: (D)

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.