A parabola `y=a x^2+b x+c` crosses the x-axis at `(alpha,0)(beta,0)` both to the right of the origin. A circle also passes through these two points. The length of a tangent from the origin to the circle is: (a) `sqrt((b c)/a)` (b) `a c^2` (c) b/a (d) `sqrt(c/a)`

Options

A. `sqrt(bc//a)`
B. `ac^(2)`
C. b/a
D. `sqrt(c//a)`

Answer

D

Explanation

(4) `OT^(2)=OA*OB=alphabeta=(c)/(a)`
`orOT=sqrt((c)/(a))`