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# Prove the following

Question:

If $3 x+4 y=12 \sqrt{2}$ is a tangent to the ellipse

$\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{9}=1$ for some $\mathrm{a} \in \mathrm{R}$, then the distance

between the foci of the ellipse is :

1. 4

2. $2 \sqrt{7}$

3. $2 \sqrt{5}$

4. $2 \sqrt{2}$

Correct Option: , 2

Solution: