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: