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Question

# A variable line is drawn through origin ′O′. Two points A and B are taken on the line in 1st quadrant such that OA=1 unit and OB=2 units. Through points A and B two lines are drawn which making an equal angle α with the line AB. Then, the locus of point of intersection of these lines is

A
x2+y2=9+tan2α4
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B
x2y2=9tan2α4
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C
x2+y2=9+tan2α2
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D
x2+y2=9+2tan2α4
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Solution

## The correct option is A x2+y2=9+tan2α4 Let C be mid point of AB Given that, AB=1 ⇒AC=CB=12⇒OC=32 and PC=12tanα⇒OP2=OC2+PC2⇒x2+y2=(32)2+14tan2α ∴x2+y2=9+tan2α4 is the required locus

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