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

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

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Solution:

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.