Let H: `x^2/a^2 -y^2/b^2 = 1, a gt 0, bgt0`, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is `4(2sqrt2 + sqrt14)` If the eccentricity H is `sqrt11/2` then the value of `a^2 + b^2` is equal to ______

The length of transverse common tangent of the circles x^2+y^2=1 and (x-h)^2+y^2=1 i s 2sqrt(3) , then the value of ' h ' is

Let the eccentricity of the hyperbola with the principal axes along the coordinate axes and passing through (3, 0) and (3sqrt2,2) is e, then the value of ((e^(2)+1)/(e^(2)-1)) is equal to

Let H :(x^2)/(a^2)-(y^2)/(b^2)=1 , where a gtb gt0 , be a hyperbola in the x y -plane whose conjugate axis L M subtends an angle of 60o at one of its vertices N . Let the area of the triangle L M N be 4sqrt(3) . LIST-I LIST-II P. The length of the conjugate axis of H is 1. 8 Q. The eccentricity of H is 2. (sqrt(4))/3 R. The distance between the foci of H is 3. 2/(sqrt(3)) S. The length of the latus rectum of H is 4. 4 The correct option is Prarr4;\ \ Qrarr2;\ \ Rrarr1;\ \ Srarr3 (b) Prarr4;\ \ Qrarr3;\ \ Rrarr1;\ \ Srarr2 (c) Prarr4;\ \ Qrarr1;\ \ Rrarr3;\ \ Srarr2 (d) Prarr3;\ \ Qrarr4;\ \ Rrarr2;\ \ Srarr1

If the eccentricity of the hyperbola x^(2)-y^(2)sec^(2)theta=4 is sqrt3 times the eccentricity of the ellipse x^(2)sec^(2)theta+y^(2)=16 , then the value of theta equals

If 2 sqrt2 x^3-3 sqrt3 y^3= (sqrt2x-sqrt 3 y)(Ax^2+ By^2+Cxy) , then the value of A^2+B^2-C^2 is:

Let frac{x^2}{a^2}+ frac{y^2}{b^2}=1 , a gt b be an ellipse, whose eccentricity is frac{1}{sqrt 2} and the length of the latus rectum is sqrt (14) . Then the square of the eccentricity of frac{x^2}{a^2}- frac{y^2}{b^2}=1 is

If a hyperbola passes through foci of the ellipse x^2/5^2 + y^2/3^2 = 1 and its transverse and conjugate axes coincide with the major and minor axes of the ellipse and the product of their eccentricities is 1, then the product of length of semi transverse and conjugate axes of hyperbola 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