JEE Main 2022 · 25 Jul · Shift 2, Mathematics question 12

If the ellipse $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ meets the line $\dfrac x7+\dfrac y{2\sqrt6}=1$ on the $x$-axis and the line $\dfrac x7-\dfrac y{2\sqrt6}=1$ on the $y$-axis, then the eccentricity of the ellipse is