locus of the point of intersection of tangents to the ellipse 2x^2+3y^2 = 6 at A and B (if AB subtend 90degrees at the centre). then the eccencentricity of the locus

x²/3 + y²/2 = 1             (in standerd form)

eq of tangent at any point to ellipse is : y = mx +(-) (a²m²+b²)^1/2

let point of intersection is (p,q) then it will satisfy the eq of tangent

  q = mp +(-) (a²m²+b²)^1/2                (a² = 3 , b²=2)

  (q - mp) = (3m²+2)^1/2

 squaring both sides & then we get a eq in terms of m ,

 m²(p²-3)  - 2mpq + q²-2 = 0       ....................1

this is quadratic in m , it is given that tangents substent 90^o at center then product of

slopes of these tangents will be = -1 ..

from eq 1 , m₁m₂ = q²-2/p²-3 = -1

  p²+q² = 5

this is eq of circle & its eccntricity is 0 ...

approve if u like my ans