If `S_(1)` and `S_(2)` are the foci of the hyperbola whose length of the transverse axis is 4 and that of the conjugate axis is 6, and `S_(3)` and `S_(4)` are the foci of the conjugate hyperbola, then the area of quadrilateral `S_(1)S_(3)S_(2)S_(4)` is

If S_1a n dS_2 are the foci of the hyperbola whose length of the transverse axis is 4 and that of the conjugate axis is 6, and S_3a n dS_4 are the foci of the conjugate hyperbola, then the area of quadrilateral S_1S_3S_2S_4 is 24 (b) 26 (c) 22 (d) none of these

Find the equation of the hyperbola whose axes are the axes of coordinates and length of conjugate axis is 5 and the distance between the foci is 13.

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci , is

Find the equation of the hyperbola, whose axes are axes of coordinates and distance between the foci is 10 and length of conjugate axis is 6.

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is : (1) 4/3 (2) 4/(sqrt(3)) (3) 2/(sqrt(3)) (4) sqrt(3)

In a hyperbola, (a) centre is origin (b) transverse axis along-with x axis (c) length of conjugates axis is 5 unit, (d) distance between two foci is 13 unit. Find the equation of the hyperbola.

In each of the find the equations of the hyperbola satisfying the given conditions. Foci (0,+-13) , the conjugate axis is of length 24 .

If S and S' are the foci of the hyperbola 4y^2 - 3x^2 = 48 and P is the any point on this hyperbola, then prove that |SP - S'P| = constant.

If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is

Normal to a rectangular hyperbola at P meets the transverse axis at N. If foci of hyperbola are S and S', then find the value of (SN)/(SP).