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Tangent To a Parabola

A parabola y=...

Question

A parabola $y = a x^{2} + b x + c$ crosses the x-axis at $(α, 0) (β, 0)$ 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{\frac{b c}{a}}

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B

a c^{2}

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C

\frac{b}{a}

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D

\sqrt{\frac{c}{a}}

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Solution

The correct option is D $\sqrt{\frac{c}{a}}$
$O T^{2} = O A . O B = α β = \frac{c}{a}$
or $O T = \sqrt{\frac{c}{a}}$

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y = a x^{2} + b x + c

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