A hyperbola, having the transverse axis of length `2sin theta`, is confocal with the ellipse `3x^2 + 4y^2=12`. Then its equation is

A hyperbola, having the transverse axis of length 2 sin theta , is confocal with the ellipse 3x^(2) + 4y^(2) = 12 . Then its equation is

A hyperbola having the transverse axis of length (1)/(2) unit is confocal with the ellipse 3x^(2)+4y^(2) = 12 , then

A hyperbola having the transverse axis of length sqrt2 units has the same focii as that of ellipse 3x^(2)+4y^(2)=12 , then its equation is

the length of the latusrectum of the ellipse 3x^(2) + y^(2) = 12 . Is

Find the equation of the hyperbola in standard form , if : it is confocal with the ellipse (x^(2)//9) + (y^(2)//5) = 1 and its eccentricity is (5/6) + eccentricity of the parabola 5y^(2) = 9x

For the ellipse 3x ^(2) + 4y ^(2) =12, the length of latus rectum is

The sum of the distances of any point on the ellipse 3x^(2)+4y^(2)=12 from its directrix is

A series of hyperbola are drawn having a common transverse axis of length 2 a.Prove that the locus of point P on each hyperbola, such that its distance from the transverse axis is equal to its distance from an asymptote,is the curve (x^(2)-y^(2))^(2)=lambda x^(2)(x^(2)-a^(2)), then lambda equals