If y = x  and  3y+2x=0 are the equations of a pair of conjugate diameters of an ellipse, then the  eccentricity of the ellipse is

: Let the equation of the ellipse be  x2/a2+y2/b2=1 Slope of the given diameters are  m1=1,m2=−2/3 ⇒m1m2=−2/3=−b2/a2[using the condition of conjugacy of two diameters] 3b2=2a2⇒3a21−e2=2a21−e2=2/3⇒e2=1/3⇒e=1/3