What will be the equation of normal to the parabola $x^{2} = - 20 y$ ?

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Solution

Given the parabola $x^{2} = - 20 y$ where $a = 5.$
We know that equation of normal to parabola of the form $x^{2} = - 4 a y$ having parametric coordinates $(2 a t, - a t^{2})$ is $x - t y = a t^{3} + 2 a t .$

So, for the parabola $x^{2} = - 20 y$ we get the equation of normal as $x - t y = 5 t^{3} + 10 t .$

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