Answer:
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.
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The curve is an ellipse.
