The differential equation of the family of curves $r^2=a^2 \cos 2 \theta$ where ' $a$ ' is an arbitrary constant is:

• A

  $\frac{d r}{d \theta}=r \cot 2 \theta$
• B

  $\frac{d r}{d \theta}=r \cdot \tan 2 \theta$
• C

  $\frac{d r}{d \theta}=r \sin 2 \theta$
• Correct answer
  D

  $\cos 2 \theta \cdot \frac{d r}{d \theta}+r \sin 2 \theta=0$

Hence, the correct answer is option: 'D'.