## What is the equation of common tangent to the parabola \(y^2\) = 4ax and \(x^2\) = 4ay ?

Solution : The equation of tangent in slope form to \(y^2\) = 4ax is y = mx + \(a\over m\) Now, if it is common to both parabola, it also lies on second parabola then \(x^2\) = 4a(mx + \(a\over m\)) \(mx^2 – 4am^2 – 4a^2\) = 0 has equal roots. then its discriminant is …

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