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Question

The point (2m,m+1) is an interior point of the smaller region bounded by the circle x2+y2=4 and the parabola y2=4x. Then m belongs to the intyerval

A
526<m<1
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B
0<m<4
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C
1<m<35
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D
1<m<5+26
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Solution

The correct option is D 1<m<5+26
When the point (2m,m+1) lies inside the region bounded by the circle and the parabola
Case - I: Point will lies inside the circle itself
S1<0
(2m)2+(m+1)24<0
5m2+2m3<0
m(1,35)(i)

Case - II: Point will lies inside the parabola also
S1<0
(m+1)24(2m)<0
m2+1+10m<0
m (526,5+26)(ii)
From equation (i) and (ii),
1<m<5+26

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