Identify whether the given equation is that of a cardioid, limaçon, rose, or lemniscate.
$r^2=-25\cos2\theta$

• A. Cardioid
• B. Limacon
• C. Rose
• D. Lemniscate

Answer: (D)

Verified step by step guidance

1. Recognize the general form of a lemniscate equation, which is typically r^2 = a^2 * cos(2θ) or r^2 = a^2 * sin(2θ).
2. Compare the given equation r^2 = -25cos(2θ) with the standard form of a lemniscate.
3. Notice that the equation matches the form r^2 = a^2 * cos(2θ) with a^2 = -25.
4. Understand that the negative sign in front of the cosine function indicates a rotation of the lemniscate.
5. Conclude that the given equation represents a lemniscate, as it fits the standard form with a negative coefficient.