Transform polar coordinates r = -4cosθ to an equation in rectangular coordinates?
How can I convert the polar equation ( r = -4\cos\theta ) into its equivalent rectangular coordinate form?
4 Answers
Use:
r = √(x^2 + y^2) and cosθ = x/r.
So we have:
r = -4cosθ
==> √(x^2 + y^2) = -4x/r, by substituting
==> √(x^2 + y^2) = -4x/√(x^2 + y^2), since r = √(x^2 + y^2)
==> x^2 + y^2 = -4x
==> (x^2 + 4x) + y^2 = 0
==> (x^2 + 4x + 4) + y^2 = 4, by completing the square
==> (x + 2)^2 + y^2 = 4 = 2^2.
This is a circle with a center of (-2, 0) and a radius of 2.
I hope this helps!
if r = -4cosθ
r^2 = -4rcosθ
now r^2 = x^2 + y^2
and x = rcosθ, so we have
x^2 + y^2 = -4x
thus
x^2 + 4x + 4 + y^2 = 4
or
(x + 2)^2 + y^2 = 4
which is a circle centered at (-2, 0) of radius 2.
r = -4cosθ
r² = -4r cosθ
Does that help? See if you can show that this is a circle, centre (-2, 0), radius 2.
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