Multiple Choice
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9. Polar Equations
Graphing Other Common Polar Equations
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Identify whether the given equation is that of a cardioid, limaçon, rose, or lemniscate.
A
Cardioid
B
Limacon
C
Rose
D
Lemniscate
Verified step by step guidance1
Step 1: Recognize the general form of polar equations. A limaçon typically has the form r = a + b cos(θ) or r = a + b sin(θ).
Step 2: Compare the given equation r = 3 + 2 cos(θ) with the general form of a limaçon. Here, a = 3 and b = 2.
Step 3: Understand the characteristics of a limaçon. If |a| > |b|, the limaçon is without an inner loop. If |a| = |b|, it is a cardioid. If |a| < |b|, it has an inner loop.
Step 4: Calculate |a| and |b| for the given equation. Here, |a| = 3 and |b| = 2, so |a| > |b|, indicating a limaçon without an inner loop.
Step 5: Conclude that the given equation r = 3 + 2 cos(θ) represents a limaçon without an inner loop based on the comparison and characteristics.
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