Question

Identify the curve by finding a Cartesian equation for the curve.

r = 2 cos θ

Answer 1

Step 1:

The equation is .

The polar coordinates are related to Cartesian coordinates by the equation .

Where .

Change the polar equation into Cartesian equation.

.

Multiply each side by .

.

Substitute and .

Change the expressions into a perfect square trinomial,

add (half the x coefficient)² to each side of the equation.

Compare above equation with circle standard equation .

Where is center of circle and is the radius of circle.

The equation is in the form of circle equation .

center of circle is .

Radius of circle is .

Solution:

The circle equation is .

center of circle is .

Radius of circle is .