If a hyperbola is confocal and coaxial with the ellipse "`(x^(2))/(4)+y^(2)=1` and intersect it at `(sqrt(3),(1)/(2))` ,then the length of transverse axis of hyperbola

If the length of minor axis of the ellipse (x^(2))/(k^(2)a^(2))+(y^(2))/(b^(2))=1 is equal to the length of transverse axis of hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 ,and the equation of ellipse is confocal with hyperbola then the value k is equal to

The length of the transverse axis of the hyperbola x^(2) -20y^(2) = 20 is

Eccentricity of a hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is " (sqrt(41))/(5), the ratio of length of transverse axis to the conjugate axis 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

If the product of the perpendicular distances from any point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 eccentricity e=sqrt(3) from its asymptotes is equal to 6, then'the length of the transverse axis of the hyperbola is

If the foci of the ellipse (x^(2))/(25)+(y^(2))/(b^(2))=1 and the hyperbola (x^(2))/(144)-(y^(2))/(81)=(1)/(25) coincide,then length of semi-minor axis is

If the hyperbola xy=4 and ellipse (x^(2))/(8)+(y^(2))/(a^(2))=1 have a commone tangent,then

If length of the transverse axis of a hyperbola is 8 and its eccentricity is sqrt(5)//2 then the length of a latus rectum of the hyperbola is

If a hyperbola passes through the focus of the ellipse x^(2)/25+y^(2)/16=1 and its transverse and conjugate gate axis coincides with the major and minor axis of the ellipse, and product of their eccentricities is 1, then