Question

How do you graph `r= 5 cos theta`?

Answer 1

Draw a circle with center at polar (5/2, 0 ) and radius 5/2.

Explanation:

r = D cos `theta` is the equation of the circle with center on the

initial line `theta` = 0, at a distance D/2. D is diameter of the circle.

The general equation of circles passing through the pole is

`r = D cos( theta -alpha) = 0`, representing the circle through r =

1. Here, the diameter is D and the center is at `( D/2, alpha )`.

The graph contrasts four such circles with D = 5 ( radius 2.5 ) and

`alpha = 0, pi/2, pi, 3/2pi`.

graph{(x^2+y^2-5x)(x^2+y^2-5y)(x^2+y^2+5x)(x^2+y^2+5y)=0[-10.2 10.2 -5.6 5.6]}