{"id":4620,"date":"2016-05-17T09:49:00","date_gmt":"2016-05-17T04:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-11-4\/"},"modified":"2016-05-17T11:34:19","modified_gmt":"2016-05-17T06:04:19","slug":"ncert-solutions-class-11-maths-exercise-11-4","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-11-4\/","title":{"rendered":"NCERT Solutions class-11 Maths Exercise 11.4"},"content":{"rendered":"

Exercise 11.4<\/strong><\/p>\n

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.<\/strong><\/p>\n

1. <\/strong><\/p>\n

Ans. <\/strong>Given: Equation of hyperbola in the form <\/p>\n

Since, the foci and vertices of the hyperbola lies on axis.<\/p>\n

<\/p>\n

and <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Coordinates of foci are <\/p>\n

<\/p>\n

Coordinates of vertices are <\/p>\n

<\/p>\n

Eccentricity <\/p>\n

Length of latus rectum = <\/p>\n

\n

2. <\/strong><\/p>\n

Ans. <\/strong>Given: Equation of hyperbola in the form <\/p>\n

Since, the foci and vertices of the hyperbola lies on axis.<\/p>\n

<\/p>\n

and <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Coordinates of foci are <\/p>\n

<\/p>\n

Coordinates of vertices are <\/p>\n

<\/p>\n

Eccentricity <\/p>\n

Length of latus rectum = <\/p>\n

\n

3. <\/strong><\/p>\n

Ans. <\/strong>Given: Equation of hyperbola <\/p>\n

<\/p>\n

in the form <\/p>\n

Since, the foci and vertices of the hyperbola lies on axis.<\/p>\n

<\/p>\n

and <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Coordinates of foci are <\/p>\n

<\/p>\n

Coordinates of vertices are <\/p>\n

<\/p>\n

Eccentricity <\/p>\n

Length of latus rectum = <\/p>\n

\n

4. <\/strong><\/p>\n

Ans. <\/strong>Given: Equation of hyperbola <\/p>\n

<\/p>\n

in the form <\/p>\n

Since, the foci and vertices of the hyperbola lies on axis.<\/p>\n

<\/p>\n

and <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Coordinates of foci are <\/p>\n

<\/p>\n

Coordinates of vertices are <\/p>\n

<\/p>\n

Eccentricity <\/p>\n

Length of latus rectum = <\/p>\n

\n

5. <\/strong><\/p>\n

Ans. <\/strong>Given: Equation of hyperbola <\/p>\n

<\/p>\n

in the form <\/p>\n

Since, the foci and vertices of the hyperbola lies on axis.<\/p>\n

<\/p>\n

and <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Coordinates of foci are <\/p>\n

<\/p>\n

Coordinates of vertices are <\/p>\n

<\/p>\n

Eccentricity <\/p>\n

Length of latus rectum = <\/p>\n

\n

6. <\/strong><\/p>\n

Ans. <\/strong>Given: Equation of hyperbola <\/p>\n

<\/p>\n

in the form <\/p>\n

Since, the foci and vertices of the hyperbola lies on axis.<\/p>\n

<\/p>\n

and <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Coordinates of foci are <\/p>\n

<\/p>\n

Coordinates of vertices are <\/p>\n

<\/p>\n

Eccentricity <\/p>\n

Length of latus rectum = <\/p>\n

\n

In each of the Exercises 7 to 15, find the equation of the hyperbola satisfying the given conditions.<\/strong><\/p>\n

7. Vertices <\/strong> foci <\/strong><\/p>\n

Ans. <\/strong>Given: The vertices lie on axis.<\/p>\n

The equation of hyperbola in standard form is <\/p>\n

is <\/p>\n

<\/p>\n

Foci is <\/p>\n

<\/p>\n

<\/p>\n

Also = <\/p>\n

Therefore, the required equation of hyperbola is <\/p>\n

.<\/p>\n

\n

8. Vertices <\/strong> foci <\/strong><\/p>\n

Ans. <\/strong>Given: The vertices lie on axis.<\/p>\n

The equation of hyperbola in standard form is <\/p>\n

is <\/p>\n

<\/p>\n

Foci is <\/p>\n

<\/p>\n

<\/p>\n

Also = <\/p>\n

Therefore, the required equation of hyperbola is <\/p>\n

.<\/p>\n

\n

9. Vertices <\/strong> foci <\/strong><\/p>\n

Ans. <\/strong>Given: The vertices lie on axis.<\/p>\n

The equation of hyperbola in standard form is <\/p>\n

is <\/p>\n

<\/p>\n

Foci is <\/p>\n

<\/p>\n

<\/p>\n

Also = <\/p>\n

Therefore, the required equation of hyperbola is <\/p>\n

.<\/p>\n

\n

10. Foci <\/strong> the transverse axis is of length 8.<\/strong><\/p>\n

Ans. <\/strong>Given: The foci lie on axis.<\/p>\n

The equation of hyperbola in standard form is <\/p>\n

Length of transverse axis: <\/p>\n

<\/p>\n

Foci is <\/p>\n

<\/p>\n

<\/p>\n

Also = <\/p>\n

Therefore, the required equation of hyperbola is <\/p>\n

.<\/p>\n

\n

11. Foci <\/strong> the conjugate axis is of length 24.<\/strong><\/p>\n

Ans. <\/strong>Given: The foci lie on axis.<\/p>\n

The equation of hyperbola in standard form is <\/p>\n

Length of conjugate axis: <\/p>\n

<\/p>\n

Foci is <\/p>\n

<\/p>\n

<\/p>\n

Also <\/p>\n

<\/p>\n

<\/p>\n

Therefore, the required equation of hyperbola is <\/p>\n

.<\/p>\n

\n

12. Foci <\/strong> the latus rectum is of length 8.<\/strong><\/p>\n

Ans. <\/strong>Given: The foci lie on axis.<\/p>\n

The equation of hyperbola in standard form is <\/p>\n

Foci is <\/p>\n

<\/p>\n

Length of latus rectum: <\/p>\n

<\/p>\n

Also <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

[ not possible]\n

<\/p>\n

<\/p>\n

Length of latus rectum: <\/p>\n

<\/p>\n

Therefore, the required equation of hyperbola is .<\/p>\n

\n

13. Foci <\/strong> the latus rectum is of length 12.<\/strong><\/p>\n

Ans. <\/strong>Given: The foci lie on axis.<\/p>\n

The equation of hyperbola in standard form is <\/p>\n

Foci is <\/p>\n

<\/p>\n

Length of latus rectum: <\/p>\n

<\/p>\n

Also <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

[ not possible]\n

<\/p>\n

<\/p>\n

Length of latus rectum: <\/p>\n

<\/p>\n

Therefore, the required equation of hyperbola is .<\/p>\n

\n

14. Vertices <\/strong><\/p>\n

Ans. <\/strong>Given: The vertices lie on axis.<\/p>\n

The equation of hyperbola in standard form is <\/p>\n

Vertices is <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Also <\/p>\n

<\/p>\n

<\/p>\n

Therefore, the required equation of hyperbola is <\/p>\n

.<\/p>\n

\n

15. Foci <\/strong> passing through (2, 3).<\/strong><\/p>\n

Ans. <\/strong>Given: The foci lie on axis.<\/p>\n

The equation of hyperbola in standard form is <\/p>\n

Foci is <\/p>\n

<\/p>\n

Also <\/p>\n

<\/p>\n

<\/p>\n

Since given hyperbola passes through (2, 3)<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

= [which is not possible]\n

And <\/p>\n

Therefore, the required equation of hyperbola is .<\/p>\n","protected":false},"excerpt":{"rendered":"

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 … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,281],"tags":[],"class_list":["post-4620","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions"],"yoast_head":"\nNCERT Solutions class-11 Maths Exercise 11.4 | myCBSEguide<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-11-4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions class-11 Maths Exercise 11.4 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"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 ... 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