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Question

The condition that the straight line joining the origin to the points of intersection of the line $$4x + 3y = 24$$ with the circle $$(x - 3)^{2} + (y - 4)^{2} = 25$$.


A
Are coincident
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B
Are perpendicular
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C
Make equal angle with x-axis
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D
None of the above
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Solution

The correct option is A Are perpendicular
Line  $$4x+3y=24$$ passes through the centre of the circle$$(x-3)^2+(y-4)^2=25$$ and intersect the circle at points $$(0,8) \text{ and }(6,0)$$.
$$\therefore$$ the lines which are joining 0rigin to (0,8) and (6,0) are perpendicular.



708852_663391_ans_9f1bc3e9f3974e18bda294b3f153cbaa.png

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