Question

find the parametrization for the circle with center at (-3,2) and with radius = 3

Answer 1

start with rectangular equation for circle
\[(x+3)^{2} + (y-2)^{2} = 9\]
then note that goal is to get it in this form:
9(sin^2 + cos^2) = 9 since the trig identity sin^2 + cos^2 = 1
\[x = 3\cos(t) -3\]
\[y=3\sin(t)+2\]
if you plug these values in you get:
\[9\cos^{2} (t) + 9\sin^{2} (t) = 9\]

Answer 2

in general for any circle with center (h,k)
\[x = r*\cos(t) +h\]
\[y = r*\sin(t)+k\]

Answer 3

oh sso x=3cos -3 and y=3sin + 2 is the ansswer ... i thoiught u had to have it equaling t thatr what i did wrong

Answer 4

ty ssmart cow