My teacher asked us to find the points on the parametric curve where the tangent

Question

My teacher asked us to find the points on the parametric curve where the tangent is horizontal AND vertical. My question is how that is even impossible. Because given the equation: dy/dx= (dy/dt)/(dx/dt) we know that there is a vertical tangent when dx/dt=0 and a horizontal tangent when dy/dt=0. So I would think that to have a vertical and horizontal tangent at the same place both dy/dt and dx/dt would have to be equal to 0. But then thats 0/0 which until now I've known that I've really screwed up in some other step if I got there. I hope this makes sense, thnaks for your help in advance.

Explanation / Answer

I don't think that's what the professor asked.

I'm absolutely sure he asked to find the points where the parametric curve has horizontal tangents

and the points where the parametric curve has vertical tangents.

He/She is not asking to find the points where the tangent line is horizontal and vertical

because there is no such thing.

I'm absolutely sure the question being asked is to find when dy/dt = 0, with dx/dt not equal to 0

and dx/dt = 0 with dy/dt not being 0.

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