Question

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

Answer 1

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`

Explanation:

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. .

graph{((x^2+y^2)^0.5-x-4)(x+4)=0}#