Question

The equation r=3cosθ represents a circle. Find the cartesian coordinates of the center, x=?,y=?, and radius=?

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 .

Step 2:

Convert the equation in standard form.

Change the expression 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 .