If the line x-2y=12 is tangent to the ellipse x^2/a^2+y^2/b^2 =1 at the point (3,-9/2) then the length of latus rectum be=?

Dear Student

Tangent at(3,−9/2​)

3x/a^2​− 9y​/2b^2=1
on Comparing this with given equation of tangent
i.e x−2y=12

3/a^2=9/4b^2=1/12​

We geta=6andb=3√3​

length of latus rectum=2b^2​/a
=9

Thanks