Problem 63E
Tracing hyperbolas and parabolas Graph the following equations. Then use arrows and labeled points to indicate how the curve is generated as θ increases from 0 to 2π.
Solution 63E
Step 1:
In this problem we have to draw the graph of r = and then use arrows and labeled points to indicate how the curve is generated as
increases from 0 to 2
.
We know that the polar equation of parabola , with focus at origin , and opening along positive x-axis.
r = , where a = distance from focus to vertex.
The graph of r = is shown below:
r = |
|
r = |
0 |
r = |
|
r = |
|
r = |
|
r =
|
2 |
As increases from 0 to 2
, the curve generated as a circle , and at
= 0 and 2
the curve approaches to infinity.