[" Let "H*(x^(2))/(a^(2))-(y^(2))/(b^(2))=1," where "a>b>0" ,be a hyperbola in the xy-plane conjugate axis LIM "],[" subtends an angle of "60^(@)" at one of its vertices "N" .Let the area of the triangle LMN be "4sqrt(3)" ."],[" LIST-I "],[" (P) The length of the conjugate axis of His "(1)8],[" (Q) The eccentricity of His "],[[" (R) The distance between the foci of His "," (3) "2/sqrt(3)],[" (S) The length of the latus rectum of His "," (4) "4]]

Let H :(x^2)/(a^2)-(y^2)/(b^2)=1 , where a > b >0 , 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 P->4;\ \ Q->2;\ \ R->1;\ \ S->3 (b) P->4;\ \ Q->3;\ \ R->1;\ \ S->2 (c) P->4;\ \ Q->1;\ \ R->3;\ \ S->2 (d) P->3;\ \ Q->4;\ \ R->2;\ \ S->1

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

The length of the hyperbola of the conjugate axis of 2x^(2) - 3y^(2) =6 is

The length of the hyperbola of the conjugate axis of 2x^(2) - 3y^(2) =6 is

The length of the conjugate axis of the hyperbola 9x^(2) -16y^(2) - 18x -64y + 89 =0 is

The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=1 is 2 (b) 2sqrt(3) (c) 4 (d) 4/5

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, eqautions of directrices and the length of latus-rectum of the hyperbola. : 3x^2-y^2=4

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, eqautions of directrices and the length of latus-rectum of the hyperbola. : x^2/25-y^2/16=1

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, eqautions of directrices and the length of latus-rectum of the hyperbola. : x^2/25-y^2/16=-1