{"id":4617,"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-11-1\/"},"modified":"2016-05-17T11:26:22","modified_gmt":"2016-05-17T05:56:22","slug":"ncert-solutions-class-11-maths-exercise-11-1","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-11-1\/","title":{"rendered":"NCERT Solutions class-11 Maths Exercise 11.1"},"content":{"rendered":"

Exercise 11.1<\/strong><\/p>\n

In each of the following Exercises 1 to 5, find the equation of the circle with:<\/strong><\/p>\n

1. Centre (0, 2) and radius 2.<\/strong><\/p>\n

Ans. <\/strong>Given: and <\/p>\n

Equation of the circle = <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

2. Centre <\/strong> and radius 4.<\/strong><\/p>\n

Ans. <\/strong>Given: and <\/p>\n

Equation of the circle = <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

3. Centre <\/strong> and radius <\/strong><\/p>\n

Ans. <\/strong>Given: and <\/p>\n

Equation of the circle = <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

4. Centre <\/strong> and radius <\/strong><\/p>\n

Ans. <\/strong>Given: and <\/p>\n

Equation of the circle: <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

5. Centre <\/strong> and radius <\/strong><\/p>\n

Ans. <\/strong>Given: and <\/p>\n

Equation of the circle = <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

In each of the following Exercises 6 to 9, find the centre and radius of the circles.<\/strong><\/p>\n

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

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

\u2026\u2026\u2026.(i)<\/p>\n

On comparing eq. (i) with <\/p>\n

and <\/p>\n

\n

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

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

<\/p>\n

<\/p>\n

<\/p>\n

\u2026\u2026\u2026.(i)<\/p>\n

On comparing eq. (i) with <\/p>\n

and <\/p>\n

\n

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

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

<\/p>\n

<\/p>\n

<\/p>\n

\u2026\u2026\u2026.(i)<\/p>\n

On comparing eq. (i) with <\/p>\n

and <\/p>\n

\n

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

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

<\/p>\n

<\/p>\n

<\/p>\n

\u2026\u2026\u2026.(i)<\/p>\n

On comparing eq. (i) with <\/p>\n

and <\/p>\n

\n

10. Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line <\/strong><\/p>\n

Ans. <\/strong>The equation of the circle is \u2026\u2026\u2026.(i)<\/p>\n

Circle passes through point (4, 1)<\/p>\n

<\/p>\n

<\/p>\n

\u2026\u2026\u2026.(ii)<\/p>\n

Again Circle passes through point (6, 5)<\/p>\n

<\/p>\n

<\/p>\n

\u2026\u2026\u2026.(iii)<\/p>\n

From eq. (ii) and (iii), we have<\/p>\n

<\/p>\n

<\/p>\n

\u2026\u2026\u2026.(iv)<\/p>\n

Since the centre of the circle lies on the line <\/p>\n

\u2026\u2026\u2026.(v)<\/p>\n

On solving eq. (iv) and (v), we have <\/p>\n

Putting the values of and in eq. (ii), we have<\/p>\n

<\/p>\n

<\/p>\n

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

<\/p>\n

<\/p>\n

<\/p>\n

\n

11. Find the equation of the circle passing through the points (2, 3) and <\/strong> and whose centre is on the line <\/strong><\/p>\n

Ans. <\/strong>The equation of the circle is \u2026\u2026\u2026.(i)<\/p>\n

Circle passes through point (2, 3)<\/p>\n

<\/p>\n

<\/p>\n

\u2026\u2026\u2026.(ii)<\/p>\n

Again Circle passes through point (\u20131, 1)<\/p>\n

<\/p>\n

<\/p>\n

\u2026\u2026\u2026.(iii)<\/p>\n

From eq. (ii) and (iii), we have<\/p>\n

<\/p>\n

<\/p>\n

\u2026\u2026\u2026.(iv)<\/p>\n

Since the centre of the circle lies on the line <\/p>\n

\u2026\u2026\u2026.(v)<\/p>\n

On solving eq. (iv) and (v), we have <\/p>\n

Putting the values of and in eq. (ii), we have<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

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

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

12. Find the equation of the circle with radius 5 whose centre lies on <\/strong>axis and passes through the point (2, 3).<\/strong><\/p>\n

Ans. <\/strong>Since the centre of circle lies on axis, therefore the coordinates of centre is <\/p>\n

Now the circle passes through the point (2, 3). According to the question,<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

or <\/p>\n

Taking , Equation of the circle is <\/p>\n

<\/p>\n

<\/p>\n

Taking , Equation of the circle is <\/p>\n

<\/p>\n

<\/p>\n

\n

13. Find the equation of the circle passing through (0, 0) and making intercept <\/strong> and <\/strong> on the coordinate axes.<\/strong><\/p>\n

Ans. <\/strong>The circle makes intercepts with axis and with axis.<\/p>\n

<\/p>\n

OA = and OB = <\/p>\n

Coordinates of A and B are and respectively.<\/p>\n

Now the circle passes through the points O (0, 0), A and B.<\/p>\n

Putting these coordinates of three points in the equation of the circle,<\/p>\n

\u2026\u2026\u2026(i)<\/p>\n

<\/p>\n

And <\/p>\n

<\/p>\n

<\/p>\n

And <\/p>\n

<\/p>\n

<\/p>\n

Putting the values of and in eq. (i), we have<\/p>\n

<\/p>\n

<\/p>\n

\n

14. Find the equation of the circle with centre (2, 2) and passes through the point (4, 5).<\/strong><\/p>\n

Ans. <\/strong>The equation of the circle is \u2026\u2026\u2026.(i)<\/p>\n

Since the circle passes through point (4, 5) and coordinates of centre are (2, 2).<\/p>\n

Radius of circle = = = <\/p>\n

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

<\/p>\n

<\/p>\n

<\/p>\n

\n

15. Does the point <\/strong> lie inside, outside or on the circle <\/strong> ?<\/strong><\/p>\n

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

<\/p>\n

On comparing with , we have and <\/p>\n

Now distance of the point from the centre (0, 0)<\/p>\n

= = = = 4.3 <5<\/p>\n

Therefore, the point lies inside the circle.<\/p>\n","protected":false},"excerpt":{"rendered":"

Exercise 11.1 In each of the following Exercises 1 to 5, find the equation of the circle with: 1. Centre (0, 2) and radius 2. Ans. Given: and Equation of the circle = 2. Centre and radius 4. Ans. Given: and Equation of the circle = 3. Centre and radius Ans. Given: and Equation of … 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-4617","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions"],"yoast_head":"\nNCERT Solutions class-11 Maths Exercise 11.1 | 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-11-1\/\" \/>\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 11.1 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Exercise 11.1 In each of the following Exercises 1 to 5, find the equation of the circle with: 1. 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