Find the points on the curve x = cos t,     y = 2 sin t,     0 leq t leq 2 pi . at which the tangent is a) horizontal, b) the tangent is vertical. what is the name of this curve?

  a) horizontal: t=π/2, 3π/2; points (0, 2), (0, -2)

  b) vertical: t=0, π; points (1, 0), (-1, 0)

  c) the curve is an ellipse

Step-by-step explanation:

The derivative of y with respect to x is ...

  dy/dx = (dy/dt)/(dx/dt) = (2cos(t))/(-sin(t))

The derivative will be zero (horizontal tangent) when cos(t)=0, at t=π/2 and 3π/2.

The derivative will be undefined (vertical tangent) when sin(t)=0, at t=0 and t=π.

__

The curve is an ellipse.

add an image

step-by-step explanation:

fyuh

step-by-step explanation:

gvfvhv