Question

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation.

r = 4

Answer 1

Step 1 :

The polar equation is .

Squaring on each side.

.

Substitute in above equation.

.

The equation in rectangular coordinates is .

Step 2 :

Identify the type of conics :

The curve is , where A and C cannot be equal to zero.

If , then the curve is a parabola.

If , then the curve is an ellipse (or) a circle.

If , then the curve a hyperbola.

The equation is .

Compare the equation with .

.

.

Since , the graph of the equation represents a circle.

The graph of the equation represents a circle with radius 4 and a center at (0, 0).

Comments

Step 3 :

The equation is .

Write the equation as .

Compare the equation with the standard form of circle : .

Center and radius .

Step 4 :

Center at (0, 0) and radius is 4.

Plot the points :

Up :

Down : 

Left : , and

Right : .

Step 5 :

1. Draw the co-ordinate plane.

2. Plot the center at (0, 0).

3. Plot 4 points " radius away from the center in the up, down, left and right direction.

4. Sketch the circle.

Graph of the equation is :

 

Solution :

The equation in rectangular coordinates is .

The graph of the equation represents a circle.

The graph is :