RD Sharma solutions for Mathematics [English] Class 11 chapter 27 - Hyperbola [Latest edition]

The equation of the directrix of a hyperbola is x − y + 3 = 0. Its focus is (−1, 1) and eccentricity 3. Find the equation of the hyperbola.

Find the equation of the hyperbola whose focus is (0, 3), directrix is x + y − 1 = 0 and eccentricity = 2 .

Find the equation of the hyperbola whose focus is (1, 1), directrix is 3x + 4y + 8 = 0 and eccentricity = 2 .

Find the equation of the hyperbola whose focus is (1, 1) directrix is 2x + y = 1 and eccentricity = \[\sqrt{3}\].

Find the equation of the hyperbola whose focus is (2, −1), directrix is 2x + 3y = 1 and eccentricity = 2 .

Find the equation of the hyperbola whose focus is (a, 0), directrix is 2x − y + a = 0 and eccentricity = \[\frac{4}{3}\].

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 axes, eccentricity, latus-rectum and the coordinates of the foci of the hyperbola 25x² − 36y² = 225.

Find the centre, eccentricity, foci and directrice of the hyperbola .

16x² − 9y² + 32x + 36y − 164 = 0

Find the centre, eccentricity, foci and directrice of the hyperbola.

 x² − y² + 4x = 0

Find the centre, eccentricity, foci and directrice of the hyperbola .

x² − 3y² − 2x = 8.

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 eccentricity of the hyperbola, the length of whose conjugate axis is \[\frac{3}{4}\] of the length of transverse axis.

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)

Find the equation of the hyperbola satisfying the given condition :

vertices (0, ± 3), foci (0, ± 5)

Find the equation of the hyperbola satisfying the given condition :

 foci (± \[3\sqrt{5}\] 0), the latus-rectum = 8

Find the equation of the hyperbola satisfying the given condition :

 foci (0, ± 13), conjugate axis = 24

find the equation of the hyperbola satisfying the given condition:

 foci (± \[3\sqrt{5}\]  0), the latus-rectum = 8

(vii)  find the equation of the hyperbola satisfying the given condition:

foci (± 4, 0), the latus-rectum = 12

find the equation of the hyperbola satisfying the given condition:

 vertices (± 7, 0), \[e = \frac{4}{3}\]

Find the equation of the hyperbola satisfying the given condition:

 foci (0, ± \[\sqrt{10}\], passing through (2, 3).

find the equation of the hyperbola satisfying the given condition:

foci (0, ± 12), latus-rectum = 36

If the distance between the foci of a hyperbola is 16 and its ecentricity is \[\sqrt{2}\],then obtain its equation.

Show that the set of all points such that the difference of their distances from (4, 0) and (− 4,0) is always equal to 2 represents a hyperbola.

Write the eccentricity of the hyperbola whose latus-rectum is half of its transverse axis.

Write the coordinates of the foci of the hyperbola 9x² − 16y² = 144.

Write the equation of the hyperbola of eccentricity \[\sqrt{2}\],  if it is known that the distance between its foci is 16.

If the foci of the ellipse \[\frac{x^2}{16} + \frac{y^2}{b^2} = 1\] and the hyperbola \[\frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25}\] coincide, write the value of b².

If the latus-rectum through one focus of a hyperbola subtends a right angle at the farther vertex, then write the eccentricity of the hyperbola.

Write the equation of the hyperbola whose vertices are (± 3, 0) and foci at (± 5, 0).

If e₁ and e₂ are respectively the eccentricities of the ellipse \[\frac{x^2}{18} + \frac{y^2}{4} = 1\]

and the hyperbola \[\frac{x^2}{9} - \frac{y^2}{4} = 1\] then write the value of 2 e₁² + e₂².

Equation of the hyperbola whose vertices are (± 3, 0) and foci at (± 5, 0), is

If e₁ and e₂ are respectively the eccentricities of the ellipse \[\frac{x^2}{18} + \frac{y^2}{4} = 1\] and the hyperbola \[\frac{x^2}{9} - \frac{y^2}{4} = 1\] , then the relation between e₁ and e₂ is

The distance between the directrices of the hyperbola x = 8 sec θ, y = 8 tan θ, is

The equation of the conic with focus at (1, −1) directrix along x − y + 1 = 0 and eccentricity \[\sqrt{2}\] is

The eccentricity of the conic 9x² − 16y² = 144 is 

A point moves in a plane so that its distances PA and PB from two fixed points A and B in the plane satisfy the relation PA − PB = k (k ≠ 0), then the locus of P is

The eccentricity of the hyperbola whose latus-rectum is half of its transverse axis, is 

The eccentricity of the hyperbola x² − 4y² = 1 is 

The difference of the focal distances of any point on the hyperbola is equal to

The foci of the hyperbola 9x² − 16y² = 144 are

The distance between the foci of a hyperbola is 16 and its eccentricity is \[\sqrt{2}\], then equation of the hyperbola is

If e₁ is the eccentricity of the conic 9x² + 4y² = 36 and e₂ is the eccentricity of the conic 9x² − 4y² = 36, then

If the eccentricity of the hyperbola x² − y² sec²α = 5 is \[\sqrt{3}\]  times the eccentricity of the ellipse x² sec² α + y² = 25, then α =

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

The length of the straight line x − 3y = 1 intercepted by the hyperbola x² − 4y² = 1 is 

The latus-rectum of the hyperbola 16x² − 9y² = 144 is

The foci of the hyperbola 2x² − 3y² = 5 are

The eccentricity the hyperbola \[x = \frac{a}{2}\left( t + \frac{1}{t} \right), y = \frac{a}{2}\left( t - \frac{1}{t} \right)\] is

The equation of the hyperbola whose centre is (6, 2) one focus is (4, 2) and of eccentricity 2 is

The locus of the point of intersection of the lines \[\sqrt{3}x - y - 4\sqrt{3}\lambda = 0 \text { and } \sqrt{3}\lambda  + \lambda - 4\sqrt{3} = 0\]  is a hyperbola of eccentricity