Question 103468
Using EXCEL, the formula, and the chart wizard, this formula yields a hyperbola. 
A conic in polar coordinates has the following form:
{{{r = pe/(1+- e sin((theta)))}}}
where p is the directix and e is the eccentricity. 
Your equation is 
{{{r= (6)/(2+4 sin (theta))}}}
{{{r= (3)/(1+2 sin (theta))}}} Take 2 out of numerator and denominator. 
{{{e=2}}} Compare to polar conic form. 
sin(theta) in the denominator denotes a vertical transverse axis. 
e>1 denotes a hyperbola. 
The directrix lies on y=p or y=3/2. 
The conic is a hyperbola with eccentricity, e=2, and directrix of y=p.