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

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Answer 1 · 2018-07-27T15:42:23

See graph and explanation.

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

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

$r = \sqrt{x^{2} + y^{2}} \geq 0 and (x, y) = r (cos θ, sin θ)$ $r = sqrt( x^2 + y^2 ) >= 0 and ( x, y ) = r ( cos theta, sin theta )$ .

The Socratic graph of this circle,

with center at $(4, - 1)$ $( 4, - 1 )$ and radius $\sqrt{17}$ $sqrt(17)$ .

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

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