Identify the conic that this polar equation represents. Also, give the position of the directix.

Question

Identify the conic that this polar equation represents. Also, give the position of the directix.
r=3/(4-2costheta)

The equation defines a circle.
The equation defines a parabola.
The equation defines a hyperbola.
The equation defines an ellipse.


The directix is____ to the polar axis and_____ unit(s)______ the pole.

Answer 1

r = 3(4-2cosT)

4r -2rcosT = 3

4sqr(x^2+y^2) -2x =3

16x^2 +16y^2 -2x =3

16x^2 +16(y^2 -x/8 + 1/16^2)= 3 + 16/256

16x^2 + 16(y^2 - 1/16) = 16/256 +3= 784/256

x^2 + (y^2 -1/16) = 784/256

is a circle with center (0, 1/16)

radius = (sqr784)/16

circles don't have directrices