Which conic section is represented by the polar equation r= 1/3+3sinθ
r = 1 / [3 + 3 sin θ]
3r = 1 / [ 1 + sinθ]
3r = 1 / [ 1 + y /r]
3r = r / [ r + y]
r + y = 1/3
r = (1/3) - y
√[x^2 + y^2] = (1/3) - y square both sides
x^2 + y^2 = 1/9 - (2/3)y + y^2
x^2 = 1/9 - (2/3)y
9x^2 = 1 + 6y
6y = -9x^2 + 1
y = (-3/2)x^2 + 1/6
This is a parabola ... see here : https://www.desmos.com/calculator/m0v1m8zsrd
Nice work Chris!
Quilly, if this is what you intended, and I expect it is, then you need to learn to use BRACKETS
I read it as you had written it which is y= 1/3 + 3sin(theta)
And so there is no way I could have given this answer!
You are lucky that CPhill has been practicing his forensic mathematics!