What is the standard form in polar equation of circle and cartiode?

Question

the circle that doesnt have its center at (0,0), and plz tell me what each variable in standard form equation means in relation to graphing it, i missed some notes, thx

Answer 1

A circle that DOES have its center at the origin with radius =c
would be r = c

Another circle with a different center would be
r = cos theta
( a circle just to the right of the vertical axis)

Another
r = sin theta
( a circle just above the horizontal axis).


A cardioid ("heart shaped figure) would have another equation
r = 1 + cos theta

see how it resembles the circle above!!!!


see wikipedia article "cardioid"

Answer 2

Remember the identities.
x = rcosθ
y = rsinθ
x² + y² = r²

Let's work out an example of the polar equation of a circle with center (3,5) and radius 2.

(x - 3)² + (y - 5)² = 4
x² - 6x + 9 + y² - 10y + 25 = 4
(x² + y²) - 6x - 10y + 30 = 0

r² - 6rcosθ - 10rsinθ + 30 = 0
r² - r(6cosθ + 10sinθ) + 30 = 0

r = {(6cosθ + 10sinθ) ± √[(6cosθ + 10sinθ)² - 4*1*30]} / 2
r = {(6cosθ + 10sinθ) ± √[(6cosθ + 10sinθ)² - 120]} / 2