Find the (i) lengths of the axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity and (v) length of the rectum of each of the following the hyperbola :

Find the (i) lengths of the axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity and (v) length of the rectum of each of the following the hyperbola :

Find the (i) lengths of the axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity and (v) length of the rectum of each of the following the hyperbola :

x² – y² = 1

Find the (i) lengths of the axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity and (v) length of the rectum of each of the following the hyperbola :

3x² – 2y² = 6

Find the (i) lengths of the axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity and (v) length of the rectum of each of the following the hyperbola :

25x² – 9y² = 225

Find the (i) lengths of the axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity and (v) length of the rectum of each of the following the hyperbola :

24x² – 25y² = 600

Find the (i) lengths of the axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity and (v) length of the rectum of each of the following the hyperbola :

Find the (i) lengths of the axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity and (v) length of the rectum of each of the following the hyperbola :

Find the (i) lengths of the axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity and (v) length of the rectum of each of the following the hyperbola :

3y² – x² = 108

Find the (i) lengths of the axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity and (v) length of the rectum of each of the following the hyperbola :

5y² – 9x² = 36

Find the equation of the hyperbola with vertices at (±6, 0) and foci at (±8, 0).

Find the equation of the hyperbola with vertices at (0, ±5) and foci at (0, ±8).

Find the equation of the hyperbola whose foci are and the transverse axis is of the length 10.

Find the equation of the hyperbola whose foci are (±5, 0) and the conjugate axis is of the length 8. Also, find its eccentricity.

Find the equation of the hyperbola whose foci are and the length of the latus rectum is 8 units.

Find the equation of the hyperbola whose vertices are (±2, 0) and the eccentricity is 2.

Find the equation of the hyperbola whose foci are and the eccentricity is .

Find the equation of the hyperbola, the length of whose latus rectum is 4 and the eccentricity is 3.

Find the equation of the hyperbola with eccentricity and the distance between whose foci is 16.

Find the equation of the hyperbola whose vertices are (0, ±3) and the eccentricity is . Also, find the coordinates of its foci.

Find the equation of the hyperbola whose foci are (0, ±13) and the length of whose conjugate axis is 24.

Find the equation of the hyperbola whose foci are (0, ±10) and the length of whose latus rectum is 9 units.

Find the equation of the hyperbola having its foci at and passing through the point P(3, 4).