How do you graph r=4costheta-2r=4cosθ−2?

2 Answers
Shwetank Mauria
Jul 23, 2016

This is a circle with center at (2,0)(2,0) and radius sqrt2√2. It's equation in rectangular form is x^2+y^2-4x+2=0x2+y2−4x+2=0.

Explanation:

To graph r=4costheta-2r=4cosθ−2 let us convert it into rectangular coordinates.

The relation between polar coordinates (r,theta)(r,θ) and rectangular coordinates (x,y)(x,y) are given by x=rcosthetax=rcosθ and y=rsinthetay=rsinθ and hence r=sqrt(x^2+y^2)r=√x2+y2

Hence r=4costheta-2r=4cosθ−2 is nothing but

rxxr=4costhetaxxr-2rr×r=4cosθ×r−2r or

x^2+y^2=4x-2sqrt(x^2+y^2)x2+y2=4x−2√x2+y2 or

graph{x^2+y^2=4x-2sqrt(x^2+y^2) [-4, 4, -2, 2]}

Zor Shekhtman
Jul 25, 2016

See the graph below

Explanation:

The graph looks like this:
enter image source here

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