im trying to find the unit tangent vector of an elipse of the form
at
Do i firstly need to get the coordinates in non-parametric form i.e.
use the equation of an elipse?
Well, if you consider a circle to be a special case of an ellipse?
If you meant , then you can do the following: [tex]\frac{dy}{dx}= \frac{\frac{dy}{dt}}{\frac{dx}{dt}= \frac{b cos(t)}{-a sin(t)}[tex]. At , [tex] and so the slope does not exist. The tangent line at is the vertical line x= -a. The unit tangent vector is .