Find equation of the normal to the parabola \( y^{2}=4 a x \) at the point \( \left(a t^{2}, 2 a t\right) \). If this normal passes through the point \( (6 a, 0) \), find the possible values of \( t \).
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Given the equation of the parabola \( y^2 = 4ax \), differentiate implicitly with respect to \( x \): \[ 2y \frac{dy}{dx} = 4a \] \[ \frac{dy}{dx} = \frac{4a}{2y} = \frac{2a}{y} \] Show more…
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