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**Exercise 11.4**

**In each of the Exercises 1 to 6, find the coordinates of the foci, and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.**

**1. **

**Ans. **Given: Equation of hyperbola in the form

Since, the foci and vertices of the hyperbola lies on axis.

and

Coordinates of foci are

Coordinates of vertices are

Eccentricity

Length of latus rectum =

**2. **

**Ans. **Given: Equation of hyperbola in the form

Since, the foci and vertices of the hyperbola lies on axis.

and

Coordinates of foci are

Coordinates of vertices are

Eccentricity

Length of latus rectum =

**3. **

**Ans. **Given: Equation of hyperbola

in the form

Since, the foci and vertices of the hyperbola lies on axis.

and

Coordinates of foci are

Coordinates of vertices are

Eccentricity

Length of latus rectum =

**4. **

**Ans. **Given: Equation of hyperbola

in the form

Since, the foci and vertices of the hyperbola lies on axis.

and

Coordinates of foci are

Coordinates of vertices are

Eccentricity

Length of latus rectum =

**5. **

**Ans. **Given: Equation of hyperbola

in the form

Since, the foci and vertices of the hyperbola lies on axis.

and

Coordinates of foci are

Coordinates of vertices are

Eccentricity

Length of latus rectum =

**6. **

**Ans. **Given: Equation of hyperbola

in the form

Since, the foci and vertices of the hyperbola lies on axis.

and

Coordinates of foci are

Coordinates of vertices are

Eccentricity

Length of latus rectum =

**In each of the Exercises 7 to 15, find the equation of the hyperbola satisfying the given conditions.**

**7. Vertices **** foci **

**Ans. **Given: The vertices lie on axis.

The equation of hyperbola in standard form is

is

Foci is

Also =

Therefore, the required equation of hyperbola is

.

**8. Vertices **** foci **

**Ans. **Given: The vertices lie on axis.

The equation of hyperbola in standard form is

is

Foci is

Also =

Therefore, the required equation of hyperbola is

.

**9. Vertices **** foci **

**Ans. **Given: The vertices lie on axis.

The equation of hyperbola in standard form is

is

Foci is

Also =

Therefore, the required equation of hyperbola is

.

**10. Foci **** the transverse axis is of length 8.**

**Ans. **Given: The foci lie on axis.

The equation of hyperbola in standard form is

Length of transverse axis:

Foci is

Also =

Therefore, the required equation of hyperbola is

.

**11. Foci **** the conjugate axis is of length 24.**

**Ans. **Given: The foci lie on axis.

The equation of hyperbola in standard form is

Length of conjugate axis:

Foci is

Also

Therefore, the required equation of hyperbola is

.

**12. Foci **** the latus rectum is of length 8.**

**Ans. **Given: The foci lie on axis.

The equation of hyperbola in standard form is

Foci is

Length of latus rectum:

Also

[ not possible]

Length of latus rectum:

Therefore, the required equation of hyperbola is .

**13. Foci **** the latus rectum is of length 12.**

**Ans. **Given: The foci lie on axis.

The equation of hyperbola in standard form is

Foci is

Length of latus rectum:

Also

[ not possible]

Length of latus rectum:

Therefore, the required equation of hyperbola is .

**14. Vertices **

**Ans. **Given: The vertices lie on axis.

The equation of hyperbola in standard form is

Vertices is

Also

Therefore, the required equation of hyperbola is

.

**15. Foci **** passing through (2, 3).**

**Ans. **Given: The foci lie on axis.

The equation of hyperbola in standard form is

Foci is

Also

Since given hyperbola passes through (2, 3)

= [which is not possible]

And

Therefore, the required equation of hyperbola is .

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