Q.31 - Calculus

Question

Graph the equations in Exercises 25–32 in the polar plane. Compare your graphs with the corresponding graphs in Exercises 17–24.

$r=sec\theta$

Step-by-Step Solution

Answer

The required graph is as follows,

Step 1. Given Information.

The polar equation is $r=sec\theta$.

Step 2. Explanation.

Make a table.

$\theta$	$0$	$\pi$	$2\pi$
$r=sec\theta$	1	-1	1

Step 3. Draw the graph.

The required graph is as follows,

Step 4. Compare the graph.

The graph of equation in polar plane is a vertical line parallel to y-axis at distance 1 unit and the graph in $\theta r-plane$is as follows.

As we have seen in both the graphs,  it is observed that one graph is plotted in polar form and one graph is plotted in algebraic form. Both the graphs are different.