Parametric equation problem...helps.......

A particle is moving in a curve according to the parametric equations x=3cos t ,y=2sin t , for 0
Question
a, In which direction is the particle moving?
b, Find the equation of the line tangent to the ellipse at time t.
c. Find the x and y intercepts of the tangent line, and state the area of the triangle formed by the origin o and the intercepts.

When t = 0, the particle is at (3, 0)
When t = π/2, it is at (0, 2)
Hence the particle moves anticlockwise around the elliptical arc.

b. dx/dt = -3 sin t; dy/dt = 2 cos t
Hence dy/dx = -(2/3) tan t
Eq of tan is thus

y - 2 sin t = -(2/3)(tan t)(x - 3 cos t)
Multiply by 3 cos t:

3y cost - 6 sint cost = -2x sint + 6 sint cost
2x sint + 3y cost - 12 sint cost = 0
i.e.
2x sint + 3y cost - 6 sin(2t) = 0

c. This line meets the x axis (y=0)
where x = 6 cost
and the y axis (x=0)
where y = 4 sint
i.e. the points are (6 cost, 0) and (0, 4 sint)
Area of triangle
= (1/2)(6 cost)(4 sint)
= 12 sint cost

the answer is wrong, the dy/dx should be -2 cost/3 sint

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