The number of lines which pass through the po | vedclass

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Question

(D) Let the point $P = (2, -3)$ and the point $Q = (-1, 2)$.Any line passing through $P$ will have a distance from $Q$ that is at most the distance $P

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(D) Let the point $P = (2, -3)$ and the point $Q = (-1, 2)$.Any line passing through $P$ will have a distance from $Q$ that is at most the distance $PQ$.The distance $PQ = \sqrt{(2 - (-1))^2 + (-3 - 2)^2} = \sqrt{3^2 + (-5)^2} = \sqrt{9 + 25} = \sqrt{34}$.Since $\sqrt{34} \approx 5.83$, and we are looking for a line at a distance of $8$ from $Q$, we note that $8 > \sqrt{34}$.Because the perpendicular distance from a point to a line cannot exceed the distance between the point and a fixed point on the line, no such line exists.Thus, the number of such lines is $0$.

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

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