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If $(α, β)$ is a point on the chord $P Q$ of the circle $x^{2} + y^{2} = 25$ , where the coordinates of $P$ and $Q$ are $(3, - 4)$ and $(4, 3)$ respectively, then

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$- 4 \leq α \leq 3 and 3 \leq β \leq 4$

none of these

$3 \leq α \leq 4 and - 4 \leq β \leq 3$

$α = 3 and - 4 \leq β \leq 4$

answer is A.

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Detailed Solution

If $(α, β)$ is a point on the chord $P Q$ , then either it is the interior point or one of the end-points of the chord $P Q$ .

$∴ 3 \leq α \leq 4 and - 4 \leq β \leq 3$ .

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