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```        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
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6 years ago

510 Points
```										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 90o 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
```
6 years ago
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