• # question_answer If the line $x2y=12$is tangent to the ellipse $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$at the point $\left( 3,\frac{-9}{2} \right),$then the length of the latus recturm of the ellipse is : [JEE Main 10-4-2019 Morning] A) $9$     B) $8\sqrt{3}$C) $12\sqrt{2}$              D) $5$

Tangent at$\left( 3,-\frac{9}{2} \right)$ $\frac{3x}{{{a}^{2}}}-\frac{9y}{2{{b}^{2}}}=1$ Comparing this with $x2y=12$ $\frac{3}{{{a}^{2}}}=\frac{9}{4{{b}^{2}}}=\frac{1}{12}$ we get a = 6 and $b=3\sqrt{3}$ $L(LR)=\frac{2{{b}^{2}}}{a}=9$