Describe the similarities and differences between the parametric equations x = t, y = t2 and x = −t, y = t2, where t ≥ 0 in each case.

Solution 6E

Step 1:

Given that

x = t, y = t2 and x = −t, y = t2, where t ≥ 0 in each case.

Step2:

To find

Describe the similarities and differences between the parametric equations.

Step3:

The similarities between the parametric equations

Both equations are parametric equation of parabola.

Step4:

The differences between the parametric equations

Both equations are mirror image of each other. The first one is parametric equation of upward opening and other one is parametric equation of downward opening.