y = x2 + ax + 1 is a parabola. its tangent @ the point of intersection at the y axis also touches the circle x2 + y2 = r2 . given tht no point of the parabola is below the y axis.
find maximum value of 'r'
262since the parabola is above x axis (q. needs to be modified)
D<0
or a2-4<0
|a|<2
dy/dx = 2x + a
at x=0,y=1, dy/dx=a
eqn of tangent is, y-1=a(x-0)
or y= ax+1.
now this is a tangent to x2 + y2 = r2
hence perp. dist. of tangent from origin =r.
or, 0+0+1√1+a2=r
now |a|<2
hence r is max at a=0
hence r max =1/1 =1
1D<0 means the discriminant of the equation is less than 0....so it does not cut the x-axis at any point....
