Solved: "What is the name of the shape graphed..."

Sylvia Macias

Answered question

2023-01-01

What is the name of the shape graphed by the function

r = 2 \cos θ

madwindnhe

Beginner2023-01-02Added 7 answers

The given equation is in polar coordinates

(r, θ)

and relation between polar coordinates and Cartesian coordinates

(x, y)

is given by

x = r \cos θ

and

y = r \sin θ

i.e.

x^{2} + y^{2} = r^{2}

Then

r = 2 \cos θ

can be written as

r^{2} = 2 r \cos θ

i.e.

x^{2} + y^{2} = 2 x

x^{2} + y^{2} - 2 x = 0

{(x - 1)}^{2} + y^{2} = 1^{2}

Thus,

r = 2 \cos θ

represents a circle with centre (1,0) and radius 1 and (1,0) in polar coordinates too is (1,0).

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