PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

Find the equation of the hyperbola whose focus is (2, 2), directrix is x + y = 9 and eccentricity = 2.

Find the eccentricity, coordinates of the foci, equation of directrice and length of the latus-rectum of the hyperbola .

9x² − 16y² = 144

Find the eccentricity, coordinates of the foci, equation of directrice and length of the latus-rectum of the hyperbola .

16x² − 9y² = −144

Find the eccentricity, coordinates of the foci, equation of directrice and length of the latus-rectum of the hyperbola .

 4x² − 3y² = 36

Find the eccentricity, coordinates of the foci, equation of directrice and length of the latus-rectum of the hyperbola .

 3x² − y² = 4 

Find the eccentricity, coordinates of the foci, equation of directrice and length of the latus-rectum of the hyperbola .

2x² − 3y² = 5.

Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in  the distance between the foci = 16 and eccentricity = \[\sqrt{2}\].

Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in  the  conjugate axis is 5 and the distance between foci = 13 .

Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in  the conjugate axis is 7 and passes through the point (3, −2).

Find the equation of the hyperbola whose foci are (6, 4) and (−4, 4) and eccentricity is 2.

Find the equation of the hyperbola whose vertices are (−8, −1) and (16, −1) and focus is (17, −1).

Find the equation of the hyperbola whose  foci are (4, 2) and (8, 2) and eccentricity is 2.

Find the equation of the hyperbola whose vertices are at (0 ± 7) and foci at \[\left( 0, \pm \frac{28}{3} \right)\] . 

Find the equation of the hyperbola whose vertices are at (± 6, 0) and one of the directrices is x = 4.

Find the equation of the hyperbola whose foci at (± 2, 0) and eccentricity is 3/2. 

Find the equation of the hyperboala whose focus is at (5, 2), vertex at (4, 2) and centre at (3, 2).

Find the equation of the hyperboala whose focus is at (4, 2), centre at (6, 2) and e = 2.

If P is any point on the hyperbola whose axis are equal, prove that SP. S'P = CP².

Find the equation of the hyperbola satisfying the given condition :

vertices (± 2, 0), foci (± 3, 0)

Find the equation of the hyperbola satisfying the given condition :

 vertices (0, ± 5), foci (0, ± 8)