Graph the polar equation: r = 12/(3 + 3 sin θ).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 63E
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Graph the polar equation: r = 12/(3 + 3 sin θ).

Expert Solution
Step 1

rewriting the equation by dividing the numerator and denominator by 3 we get 

r=12/333+33sinθr=41+sinθ

Step 2

here we can see that e = 1 so the graph will be in a parabola shape and the focus is at the origin.

The function has a sinθsinθ term and there is an addition sign in the denominator, so the directrix is y=p.

4 = ep

4 = (1)p

4 = p

so, the directix will be y = 4 

 

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