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Question

A variable line L is drawn through O(0,0) to meet the linesL1:YX10=0 And L2:YX20=0 . At points A And B Respectively. A Point P is taken on L such that 2OP=1OA+1OB And P,A,B lies on the same side of originO. The locus of P is


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Solution

Let, the given value of x&y are,

x=rcosθy=rsinθ

Now, by substituting in L1 we get,

1OA=sinθ-cosθ10

Now, by substituting inL2, we get,

1OB=sinθ-cosθ20

Therefore,

2r=sinθ-cosθ10+sinθ-cosθ20

40=3rsinθ-3cosθ=3y-3x

Therefore, the Locus of P is 3y-3x=40


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