Which conic section is represented by the polar equation r= 1/3+3sinθ

hyperbola

parabola

circle

ellipse

quilly
Mar 28, 2018

#1**+3 **

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

CPhill
Mar 28, 2018

#2**+2 **

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!

Melody
Mar 28, 2018