Translating polar graphs?

Question

Hey everyone,
In math I have to create a picture(caterpillar, bear, etc.) using polar graphs. I can do many pictures and such along the origin, but I don't know how to translate the graphs. I know you have to put it into rectangular form and then convert to polar. CAn anyone help me make a circle centered at (2,4) in polar?

Also, anyone have interesting ideas for possible pictures?

Answer 1

The general polar form for an equation of a circle with radius R and center (h,k) is:

r² - 2r(hcosθ + ksinθ) = R² - h² - k²

For example, for a circle with center (h,k) = (2,4) and radius 5 the equation is:

r² - 2r(2cosθ + 4sinθ) = 5² - 2² - 4² = 25 - 4 - 16

r² - 2r(2cosθ + 4sinθ) = 5

r² - 2r(2cosθ + 4sinθ) - 5 = 0

Answer 2

r = √ (x2 + y2)

θ = atan( y / x )

http://www.mathsisfun.com/polar-cartesian-coordinates.html