Conic Sections Exercise 11.4
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 
.