If a and c are positive real number and the ellipse
Question:

If $\mathrm{a}$ and $\mathrm{c}$ are positive real number and the ellipse $\frac{\mathrm{x}^{2}}{4 \mathrm{c}^{2}}+\frac{\mathrm{y}^{2}}{\mathrm{c}^{2}}=1$ has four distinct points in common with the circle $x^{2}+y^{2}=9 a^{2}$, then

  1. $6 a c+9 a^{2}-2 c^{2}>0$

  2. $6 a c+9 a^{2}-2 c^{2}<0$

  3. $9 a c-9 a^{2}-2 c^{2}<0$

  4. $9 a c-9 a^{2}-2 c^{2}>0$


Correct Option: , 4

Solution:

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