Relative Position of a Point with Respect to a Line
If a , a 2 fa...
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:x−2y=0L2:3x−y=0 Points A and P lie on opposite side of line x−2y=0L1(1,0)=1−2(0)>0∴a−2a2<0 or a(2a−1)>0 or a>12...(i) Points A and P lie on same side of line 3x−y=0L2(1,0)=3−0>0∴3a−a2>0or(a−3)<0or0<a<3...(ii) From (i)and(ii)12<a<3