    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+2√6When 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)2−4<0 ⇒ 5m2+2m−3<0 ⇒m∈(−1,35)⋯(i) Case - II: Point will lies inside the parabola also ⇒ S1<0 ⇒ (m+1)2−4(−2m)<0 ⇒ m2+1+10m<0 ⇒m ∈ (−5−2√6,−5+2√6)⋯(ii) From equation (i) and (ii), −1<m<−5+2√6  Suggest Corrections  6      Similar questions  Related Videos   Position of a Point Relative to a Parabola
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