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Grade:
        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

8 years ago

Answers : (1)

vikas askiitian expert
509 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

8 years ago
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