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Question

If (a,a2) falls inside the angle made by the lines y=x2,x>0, and y=3x,x>0, then a belongs to

A
(0,12)
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B
(3,)
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C
(12,3)
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D
(3,12)
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Solution

The correct option is C (12,3)

Given lines
L1:x2y=0L2:3xy=0
Points A and P lie on opposite side of line x2y=0L1(1,0)=12(0)>0a2a2<0
or a(2a1)>0
or a>12 ...(i)
Points A and P lie on same side of line 3xy=0L2(1,0)=30>0 3aa2>0 or (a3)<0 or 0<a<3 ...(ii)
From (i)and(ii)12<a<3

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