I learned that vertifcal tangents occur at a parametric curve if the derivative of the curve is undefined. That is given dy/dx = dy/dt / dx/dt, a vertical tangent occurs when dx/dt = 0. I don't understand why this is so. I know that vertical tangents occur when the slope is infinite, but if dx/dt = 0, dy/dx is undefined. I understand that when the slope is infinite it is undefined, but there are cases in which the slope is undefined, and yet it is not infinite, right? Or is it true that for parametric curves, all undefined slopes are infinite?