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A parabola y = a*x² + b*x + c meets the x-axis at the points (alpha, 0) and (beta, 0), both lying to the right of the origin. A circle is drawn through these two points. Find the length of the tangent drawn from the origin to this circle.
- sqrt(c/a)
- sqrt(bc/a)
- ac²
- b/a
Correct answer: sqrt(c/a)
Solution
The tangent length from the origin equals sqrt(alpha*beta) since the x-axis is a secant through both points; alpha*beta = c/a, so the tangent length = sqrt(c/a).
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