Answer:
a. [tex]r=1+2\cos(\theta)[/tex]
Step-by-step explanation:
The curve
[tex]r=1+2\cos(\theta)[/tex]
is not a conic.
Convert to rectangular coordinates.
First multiply through by r.
[tex]r^2=r+2r\cos(\theta)[/tex]
Substitute [tex]r^2=x^2+y^2[/tex]
and
[tex]x=r\cos(\theta)[/tex]
[tex]x^2+y^2=\sqrt{x^2+y^2}+2x[/tex]
We can see clearly that this is not a conic.
[tex]r=1+2\cos(\theta)[/tex] is an equation of a cardioid.
[tex]r=3[/tex] is a circle.
[tex]r=\frac{1}{1+\sin(\theta)}[/tex] is a parabola.
[tex]r=\frac{1}{2-\cos(\theta)}[/tex] is an ellipse.
