SOLUTION: Thank you thank you thank you for all your assistance,,,love and light- Namaste! Find the eccentricity and identify the graph of the conic: r= (6)/(2+4sin theta)

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Question 103468: Thank you thank you thank you for all your assistance,,,love and light- Namaste!
Find the eccentricity and identify the graph of the conic: r= (6)/(2+4sin theta)
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
Using EXCEL, the formula, and the chart wizard, this formula yields a hyperbola.
A conic in polar coordinates has the following form:
r+=+pe%2F%281%2B-+e+sin%28%28theta%29%29%29
where p is the directix and e is the eccentricity.
Your equation is
r=+%286%29%2F%282%2B4+sin+%28theta%29%29
r=+%283%29%2F%281%2B2+sin+%28theta%29%29 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.