Help with parametric equations

[riverjib]

Can somebody help me with the following problems? For each of the following parametric curves, describe the motion of the particle. That is, tell the type of curve, the starting point of the particle, the direction of motion, and the behavior of the particle.

1. x=sect
y=tant
t= [0, pi/2)U(pi/2, 3*pi/2)

2. x^2=(sint)^2
y^2=(cost)^2
0 less than or equal to t less than or equal to 2pi

3. x=sint
y=(sint)^2
0 less than or equal to t less than or equal to 2pi

4. x=(1-t^2)/(1+t^2)
y=(2t)/(1+t^2)
t is greater than or equal to zero

 

[skeeter]

1. x² = sec²t = tan²t + 1
y² = tan²t

so ... x² = y² + 1

what does one call the graph of this equation?

2. x² + y² = sin²t + cos²t = 1

what is this a graph of?

3. y = x² ?

4. last one took a little work with the algebra ...
using the x-equation, solve for t², then t ... substitute the result into the y-equation ... I got y = sqrt(1 - x²) ... a semicircle.