Tangent to the parabola `y=x^(2)+ax+1` at the point of intersection of the y-axis also touches the circle `x^(2)+y^(2)=r^(2)`. Also, no point of the parabola is below the x-axis. The radius of circle when a attains its maximum value is

Options

A. (a) `1//sqrt(10)`
B. (b) `1//sqrt(5)`
C. (c) 1
D. (d) `sqrt(5)`

Answer

B

Explanation

(2) Since no point of the parabola is below the x-axis,
`D=a^(2)-4le0`
Therefore, the maximum value of a is 2.
The equation of the parabola when a=2 is
`y=x^(2)+2x+1`
It intersect the y-axis at (0,1).
The equation of the tangent at (0,1).
y=2x+1
Since y=2x+1 touches the circle `x^(2)+y^(2)=r^(2)`, we get
`r=(1)/(sqrt(5))`