The position vector of a particle moving in the x-y plane is vector components 2 times the cosine of t, 4 times the sine of t in the interval [0, 2π). For what value(s) of t does the path of the particle have a vertical tangent? (10 points)

Question

A) pi over 2, 3 times pi over 2
B) 0, π
C) pi over 4, 3 times pi over 4
D) None of these

Answer 1

dy/dx = (dy/dt) / (dx/dt)
for a vertical tangent, you need dx/dt = 0
so, (B)

the curve is the ellipse x^2/4 + y^2/16 = 0, so that makes sense.