Transform each polar equation to an equation in rectangular coordinates and identify its shape.
(a) r=6
(b) r= 2 cos theta

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(a)    circle centered on the point (0,0) and with a constant radius .

(b)  circle centered on the point (1, 0) and with radio

Step-by-step explanation:

Remember that to convert from polar to rectangular coordinates you must use the relationship:

In this case we have the following equations in polar coordinates.

(a) .

Note that in this equation the radius is constant, it does not  depend on .

As

Then we replace the value of the radius in the equation and we have to::

Then in rectangular coordinates is a circle centered on the point (0,0) and with a constant radius .

(b)

The radius is not constant, the radius depends on .

To convert this equation to rectangular coordinates we write

    Multiply both sides of the equality by r.

    remember that , then:

       remember that , then:

        Simplify the expression.

    Complete the square.

 It is a circle centered on the point (1, 0) and with radio