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

If the eccentricity of hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is (5)/(4) and 2x+3y-6=0 is a focal chord of hyperbola,then length of transverse axis is:

If eccentricity of the ellipse (x^(2))/(a^(2)+1)+(y^(2))/(a^(2)+2)=1 is (1)/(sqrt6) , then the ratio of the length of the latus rectum to the length of the major axis is

The eccentricity of the hyperbola (sqrt(1999))/(3)(x^(2)-y^(2))=1 , is

For hyperbola, If transverse axis = conjugate axis , then e =

Find the equation of hyperbola whose transverse axis is 10 conjugate axis is 6.

The eccentricity of the hyperbola (sqrt(2006))/(4) (x^(2) - y^(2))= 1 is

For the hyperbola (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , the normal at point P meets the transverse axis AA' in G and the connjugate axis BB' in g and CF be perpendicular to the normal from the centre. Q. Locus of middle-point of G and g is a hyperbola of eccentricity

The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the hyperbola (x^(2))/(A^(2))-(y^(2))/(B^(2))=1 are given to be confocal and length of mirror axis of the ellipse is same as the conjugate axis of the hyperbola. If e_1 and e_2 represents the eccentricities of ellipse and hyperbola respectively, then the value of e_(1)^(-2)+e_(1)^(-2) is

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 normal at P(a sec theta,b tan theta) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the transverse axis in G then minimum length of PG is