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Question

y=f(x) is the parabola of the form y=x2+ax+1, its tangent at the point of intersection of yaxis and parabola also touches the circle x2+y2=r2. It is known that no point of the parabola is below xaxis. The radius of the circle (in units) when a attains its maximum value is

A
110
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B
15
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C
1
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D
5
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Solution

The correct option is B 15
Since no point of the parabola is below xaxis.
a240
maximum value of a is 2.
Equation of parabola when a=2 is y=x2+2x+1
It intersects yaxis at (0,1).
Equation of the tangent at (0,1) is y=2x+1
Since, y=2x+1 touches the circle x2+y2=r2
r=1a2+1
r=15units

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