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Question

If the point (a,a2) lies inside the triangle formed by the lines 2x+3y−1=0, x+2y−1=0 and −8x+8y+2=0 then

A
1<a<12
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B
a>1
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C
a>13
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D
13<a<12
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Solution

The correct option is D 13<a<12

2x+3y1=0
put (0,0)
1<0
so,
2a+3a21>0

x+2y1=0
put (0,0)
1<0
so,
a+2a21<0

8x+8y+2=0
put (0,0)
2>0
so,
8a+8a2+2>0

2a+3a21>0(3a1)(a+1)>0a<1,a>13

a+2a21<0(2a1)(a+1)<01<a<12

8a+8a2+2>0(2a1)2>0a12

13<a<12


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