Determine a polar equation for the circle satisfying the giv

Determine a polar equation for the circle satisfying the given conditions. (a) The radius is 9, and the polar coordinates of the center are (9, p/2). (b) The radius is 9, and the polar coordinates of the center are (9, 3 pi/4).

Solution

a. polar coordinates (9,pi/2)

r=9 and theta=pi/2

x=r cos theta=9 cos pi/2=0

y=r sin theta=9sin pi/2=9

center (0,9)

required equation

(x-0)^2 +(y-9)^2=81

b. polar form(9,3pi/4)

x=r cos theta=-9/sqrt2

y=r sin 3pi/4=9/sqrt2

center(-9/sqrt2,9/sqrt2)

(x+9/sqrt2)^2 +(y-9/sqrt2)^2=81