##r=2(3 cos theta – 4 sin theta )##. Graph is inserted.

The conversion formula is

##(x y)=r(cos theta sin theta)##

So the polar equation is

(r cos theta- 3 )^2+(r sin theta + 4 )^2=25.

Expanding and simplifying

##r=2(3 cos theta – 4 sin theta )##

The circle passes through the pole (r = 0 )

when ##theta =tan^(-1)(3/4)=36.87^o## and also when theta =

216.87^o.

This interpretation of reaching the pole is important in the polar

frame. This discloses the directions of entry into and exit from the

pole.

graph{(x-3)^2+(y+4)^2-25=0 [-20 20 -10 10]}