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If $$\left( \alpha ,\beta \right)$$ is a point on the chord $$PQ$$ of the circle $${ x }^{ 2 }+{ y }^{ 2 }=19,$$ where the coordinate of $$P$$ and $$Q$$ are $$(3,-4)$$ and $$(4,3)$$ respectively, then
(A) $$\alpha \in \left[ 3,4 \right] ,\beta \in \left[ -4,3 \right]$$
(B) $$\alpha \in \left[ -4,3 \right] ,\beta \in \left[ 4,3 \right]$$
(C) $$\alpha \in \left[ 3,3 \right] ,\beta \in \left[ -4,4 \right]$$
(D) None of these
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## QuestionMathsClass 9

If $$\left( \alpha ,\beta \right)$$ is a point on the chord $$PQ$$ of the circle $${ x }^{ 2 }+{ y }^{ 2 }=19,$$ where the coordinate of $$P$$ and $$Q$$ are $$(3,-4)$$ and $$(4,3)$$ respectively, then
(A) $$\alpha \in \left[ 3,4 \right] ,\beta \in \left[ -4,3 \right]$$
(B) $$\alpha \in \left[ -4,3 \right] ,\beta \in \left[ 4,3 \right]$$
(C) $$\alpha \in \left[ 3,3 \right] ,\beta \in \left[ -4,4 \right]$$
(D) None of these

Clearly, the point $$\left( \alpha ,\beta \right)$$ is either an internal point or one of the end points of the line segment joining $$P(3,-4)$$ and $$Q(4,3)$$.
$$\therefore 3\le \alpha \le 4$$ and $$-4\le \beta \le 3$$