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**Exercise 11.3**

**In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.**

**1. **

**Ans. **Given: Equation of ellipse:

36 > 16

Now =

Coordinates of foci are

Coordinates of vertices are

Length of major axis = =

Length of minor axis = =

Eccentricity

Length of latus rectum =

**2. **

**Ans. **Given: Equation of ellipse:

25 > 4

Now =

Coordinates of foci are

Coordinates of vertices are

Length of major axis = =

Length of minor axis = =

Eccentricity

Length of latus rectum =

**3. **

**Ans. **Given: Equation of ellipse:

16 > 9

Now =

Coordinates of foci are

Coordinates of vertices are

Length of major axis = =

Length of minor axis = =

Eccentricity

Length of latus rectum =

**4. **

**Ans. **Given: Equation of ellipse:

100 > 25

Now =

Coordinates of foci are

Coordinates of vertices are

Length of major axis = =

Length of minor axis = =

Eccentricity

Length of latus rectum =

**5. **

**Ans. **Given: Equation of ellipse:

49 > 36

Now =

Coordinates of foci are

Coordinates of vertices are

Length of major axis = =

Length of minor axis = =

Eccentricity

Length of latus rectum =

**6. **

**Ans. **Given: Equation of ellipse:

400 > 100

Now =

Coordinates of foci are

Coordinates of vertices are

Length of major axis = =

Length of minor axis = =

Eccentricity

Length of latus rectum =

**7. **

**Ans. **Given: Equation of ellipse:

36 > 4

Now =

Coordinates of foci are

Coordinates of vertices are

Length of major axis = =

Length of minor axis = =

Eccentricity

Length of latus rectum =

**8. **

**Ans. **Given: Equation of ellipse:

16 > 1

Now =

Coordinates of foci are

Coordinates of vertices are

Length of major axis = =

Length of minor axis = =

Eccentricity

Length of latus rectum =

**9. **

**Ans. **Given: Equation of ellipse:

9 > 4

Now =

Coordinates of foci are

Coordinates of vertices are

Length of major axis = =

Length of minor axis = =

Eccentricity

Length of latus rectum =

**In each of the Exercises 10 to 20, find the equation of the ellipse that satisfies the given conditions:**

**10. Vertices **** foci **

**Ans. **Since foci lie on axis, therefore equation of ellipse is

Now Vertices

And Foci

Therefore, the required equation of ellipse is .

**11. Vertices **** foci **

**Ans. **Since foci lie on axis, therefore equation of ellipse is

Now Vertices

And Foci

Therefore, the required equation of ellipse is .

**12. Vertices **** foci **

**Ans. **Since foci lie on axis, therefore equation of ellipse is

Now Vertices

And Foci

Therefore, the required equation of ellipse is .

**13. Ends of major axis **** ends of minor axis **

**Ans. **Ends of major axis lie on axis, therefore equation of ellipse is

Now Ends of major axis

And Ends of minor of axis

Therefore, the required equation of ellipse is .

**14. Ends of major axis **** ends of minor axis **

**Ans. **Ends of major axis lie on axis, therefore equation of ellipse is

Now Ends of major axis

And Ends of minor of axis

Therefore, the required equation of ellipse is .

**15. Length of major axis 26, foci **

**Ans. **Since foci lie on axis, therefore equation of ellipse is

Length of major axis =

Foci =

Therefore, the required equation of ellipse is .

**16. Length of minor axis 16, foci **

**Ans. **Since foci lie on axis, therefore equation of ellipse is

Length of major axis =

Foci =

Therefore, the required equation of ellipse is .

**17. Foci **

**Ans. **Since foci lie on axis, therefore equation of ellipse is

Foci =

Therefore, the required equation of ellipse is .

**18. **** centre at origin; foci on ****axis**

**Ans. **Since foci lie on axis, therefore equation of ellipse is

Therefore, the required equation of ellipse is .

**19. Centre at (0, 0), major axis on the ****axis and passes through the points (3, 2) and (1, 6).**

**Ans. **Since the major axis is along axis, therefore equation of ellipse is

And the ellipse passes through the point (3, 2) therefore …..(i)

And the ellipse passes through the point (1, 6) therefore …..(ii)

Solving eq. (i) and (ii), we have

Therefore, the required equation of ellipse is .

**20. Major axis on the ****axis and passes through the points (4, 3) and (6, 2).**

**Ans. **Since the major axis is along axis, therefore equation of ellipse is

And the ellipse passes through the point (4, 3) therefore …..(i)

And the ellipse passes through the point (6, 2) therefore …..(ii)

Solving eq. (i) and (ii), we have

Therefore, the required equation of ellipse is .

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