Question

Y=f(x) is a parabola of the form y=x^2+ax+1,its tangent at the point of intersection of y axis and parabola also touches the circle

Answer 1

Answer:

Your question seem to incomplete . What is unknown ?

Answer 2

Answer:

$1/\sqrt{5}$

Step-by-step explanation:

Since no point of the parabola is below the x-axis,

D=a2−4≤0

Therefore, the maximum value of a is 2.

The equation of the parabola when a=2 is

y=x2+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 x2+y2=r2, we get

r=$\frac{1}{\sqrt{5} }$