| (a) |
Observe the curve x = r cos t, y = r sin t. Click on "Equalize axes"
to get an accurate display of the shape of the curve. Try various values of r.
Describe what happens. What is the cartesian equivalent? |
| (b) |
Extend to x =a +
r cos t, y =b + r sin t for various values of the constants a and
b. |
|
Describe fully the resulting curve, noting
particularly the significance of a, b and r. |
|
What is the cartesian equivalent
now? |
|
What are the general charactersitics
when
(i) a = r
(ii) b = r ?
Prove your answers. |
| (c) |
Return to the case x = r cos t, y = r sin t. Suppose we wish to join up
two points on this curve with a straight line. Investigate the case when the
points have parameters p and q subject to the constraint that p+q = 1. |
|
Do the same for other values of p and q
with p+q = 1. What do you notice? Prove
your answer. |
| (d) |
What if p+q =
m, where m is some other number? Does a similar effect occur? What
is the gradient of the chords when p+q =
m? |
P3.1
Based on
free Java applets from