WBCHSE Mathematics for Class 11>Chapter 20 - Hyperbola>EXERCISE 5>Q 16

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11th West Bengal Board

IMPORTANT

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The equation of the hyperbola whose vertices are $(\pm 2, 0)$ and the eccentricity is $2$ is $\frac{x^{2}}{k^{2}} - \frac{y^{2}}{12} = 1$ , then find the value of $k^{2}$ .

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Important Questions on Hyperbola

MEDIUM

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 20 - Hyperbola>EXERCISE 5>Q 17

The equation of the hyperbola whose foci are

(\pm \sqrt{5}, 0)

and the eccentricity is

\sqrt{\frac{5}{3}}

is

\frac{x^{2}}{3} - \frac{y^{2}}{k^{2}} = 1

, then find the value of

k^{2}

.

MEDIUM

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 20 - Hyperbola>EXERCISE 5>Q 18

The equation of the hyperbola, the length of whose latus rectum is

4

and the eccentricity is

3

is

k x^{2} - 2 y^{2} = 1

, then find the value of

k

.

MEDIUM

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 20 - Hyperbola>EXERCISE 5>Q 19

The equation of the hyperbola with eccentricity is

\sqrt{2}

and the distance between whose foci is

16

is

\frac{x^{2}}{k^{2}} - \frac{y^{2}}{32} = 1

, then find the value of

k^{2}

.

HARD

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 20 - Hyperbola>EXERCISE 5>Q 20

Find the equation of the hyperbola whose vertices are

(0, \pm 3)

and the eccentricity is

\frac{4}{3}

. Also find the coordinates of its foci.

MEDIUM

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 20 - Hyperbola>EXERCISE 5>Q 21

The equation of the hyperbola whose foci are

(0, \pm 13)

and the length of whose conjugate axis is

24

is

\frac{y^{2}}{25} - \frac{x^{2}}{k^{2}} = 1

, then find the value of

k

.

HARD

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 20 - Hyperbola>EXERCISE 5>Q 22

The equation of the hyperbola whose foci are

(0, \pm 10)

and the length of whose latus rectum is

9 units

is

\frac{y^{2}}{k^{2}} - \frac{x^{2}}{36} = 1

, then find the value of

k

.

HARD

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 20 - Hyperbola>EXERCISE 5>Q 23

The equation of the hyperbola having its foci at

(0, \pm \sqrt{14})

and passing through the point

(3, 4)

is

\frac{y^{2}}{k^{2}} - \frac{x^{2}}{7} = 1

, then find the value of

k^{2}

.