How do you graph # r=4/(1-costheta)#?

1 Answer
May 26, 2016

This is the polar equation of the parabola with vertex at #V (2, 0))# and focus S at the pole(r=0). The directrix is along #r cos theta = 4 #


The equation is obtained from the definition of the parabola, 'the

distance from the focus = the distance from the directrix, referred

to the focus as pole r = 0 and the focus-to-vertex axis of the

parabola as the initial line,

#theta=0# ( negative x-axis ).

The standard form is

#(semi latus rectum)/r = 1 + cos theta.#.

Here, the initial line is reversed to make it

#(semi latus rectum)/r = 1 - cos theta.#..

After converting to Cartesian frame as #sqrt(x^2 + y^2) = x + 4#, the

parabola is drawn, using Socratic graphic facility. The focus is at O.

See the directrix x + 4 = 0. .