Question

How do you graph `r=8cos(theta)-2sin(theta)`?

Answer 1

See graph and explanation.

Explanation:

Convert `r = 8 cos theta - 2 sin theta` to Cartesian form

#x^2 + y^2 - 8 x +2 y = 0, using

`r = sqrt( x^2 + y^2 ) >= 0 and ( x, y ) = r ( cos theta, sin theta )`.

The Socratic graph of this circle,

with center at `( 4, - 1 )` and radius `sqrt(17)`.

is immediate.
graph{(x^2+y^2-8x+2y)((x-4)^2+(y+1)^2-0.04)=0[-1 23 -6 6] }