Parabolic Circle

Geometry Level 4

Consider the parabola \(y=ax^2 + bx+c\), if it intersects \(x\)-axis at \(\alpha > 0 \) and \(\beta > 0 \), find the length of the tangent from the origin to the circle passing through \(\alpha\) and \(\beta\) when \(a=2, b>120, c=162\). Hint: consider\(\alpha\) and \(\beta\) to be diametric end points.

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