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Equation of Tangent at a Point (x,y) in Terms of f'(x)

If α ,β is ...

Question

If $(α, β)$ is a point on the chord $P Q$ of the circle $x^{2} + y^{2} = 19,$ where the coordinate of $P$ and $Q$ are $(3, - 4)$ and $(4, 3)$ respectively, then

α \in [3, 4], β \in [- 4, 3]

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α \in [- 4, 3], β \in [4, 3]

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α \in [3, 3], β \in [- 4, 4]

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None of these

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Solution

The correct option is C $α \in [3, 4], β \in [- 4, 3]$
Clearly, the point $(α, β)$ is either an internal point or one of the end points of the line segment joining $P (3, - 4)$ and $Q (4, 3)$ .
$∴ 3 \leq α \leq 4$ and $- 4 \leq β \leq 3$

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