Axis of symmetry of a (rotated) parabola given its parametric equation.

by Atin   Last Updated August 14, 2019 07:20 AM

Given a parabola's parametric equation I want to find it's axis of symmetry.

The parametric equation is $$\begin{cases} x=a_1t^2+b_1t+c_1 \\ y=a_2t^2+b_2t+c_2 \end{cases}, t\in\mathbb{R}.$$

This is parabola as was shown in other question.

I understand that one can start with finding the general equation from this parametric one, proceed with finding the rotation angle, getting rid of $xy$ term and finally finding an axis of symmetry.

My question is whether there is a simpler way to do this? The resulting line may also be given by a parametric equation.

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