{"id":4614,"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-10-2\/"},"modified":"2016-05-17T11:18:38","modified_gmt":"2016-05-17T05:48:38","slug":"ncert-solutions-class-11-maths-exercise-10-2","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-10-2\/","title":{"rendered":"NCERT Solutions class-11 Maths Exercise 10.2"},"content":{"rendered":"

Exercise 10.2<\/strong><\/p>\n

In Exercises 1 to 8, find the equations of the line which satisfy the given conditions:<\/strong><\/p>\n

1. Write the equations for the <\/strong> and <\/strong>axis.<\/strong><\/p>\n

Ans. <\/strong>Equation for axis is <\/p>\n

Equation for axis is <\/p>\n

\n

2. Passing through the point <\/strong> with slope <\/strong><\/p>\n

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

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

3. Passing through (0, 0) with slope <\/strong><\/p>\n

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

<\/p>\n

<\/p>\n

<\/p>\n

\n

4. Passing through <\/strong> and inclined with the <\/strong>axis at an angle of <\/strong><\/p>\n

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

Now, <\/p>\n

= <\/p>\n

= <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

5. Intersecting the <\/strong>axis at a distance of 3 units to the left of origin with slope <\/strong><\/p>\n

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

<\/p>\n

<\/p>\n

<\/p>\n

\n

6. Intersecting the <\/strong>axis at a distance of 2 units above the origin and making an angle of <\/strong> with positive direction of the <\/strong>axis.<\/strong><\/p>\n

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

<\/p>\n

<\/p>\n

<\/p>\n

\n

7. Passing through the points <\/strong> and <\/strong><\/p>\n

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

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

8. Perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive <\/strong>axis is <\/strong><\/p>\n

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

<\/p>\n

<\/p>\n

<\/p>\n

\n

9. The vertices of <\/strong>PQR are P (2, 1), Q<\/strong> and R (4, 5). Find equation of the median through the vertex R.<\/strong><\/p>\n

Ans. <\/strong>Given: P (2, 1), Q and R (4, 5) are the vertices of . RS is the median through vertex R. Then S is the mid-point of PQ.<\/p>\n

<\/p>\n

Coordinates of S are (0, 2)<\/p>\n

Equation of required median RS is<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

10. Find the equation of the line passing through <\/strong> and perpendicular to the line through the points (2, 5) and <\/strong><\/p>\n

Ans. <\/strong>Let A (2, 5) and B be any two points.<\/p>\n

Slope of AB = <\/p>\n

Since, the required line is perpendicular to AB, therefore slope of required line <\/p>\n

Also, the required line passing through point having slope 5.<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

11. A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio <\/strong> Find the equation of the line.<\/strong><\/p>\n

Ans. <\/strong>Let point C divides the join of A (1, 0) and B (2, 3) in the ratio <\/p>\n

Coordinates of C are <\/p>\n

And Slope of AB = <\/p>\n

Since, the required line is perpendicular to AB, therefore slope of required line <\/p>\n

Also, the required line passing through point having slope <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

12. Find the equation of the line cuts off equal intercepts on the coordinate axis and passes through the point (2, 3).<\/strong><\/p>\n

Ans. <\/strong>Let equal intercepts on the coordinate axis be and the line passes through point (2, 3).<\/p>\n

<\/p>\n

<\/p>\n

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

<\/p>\n

\n

13. Find the equation of the line passing through the point (2, 2) and cutting off intercept on the axis whose sum is 9.<\/strong><\/p>\n

Ans. <\/strong>Given: Line passes through point (2, 2). And <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

and <\/p>\n

and <\/p>\n

Therefore, equation of lines are<\/p>\n

<\/p>\n

and <\/p>\n

<\/p>\n

\n

14. Find equation of the line through the point (0, 2) making an angle <\/strong> with the positive <\/strong>axis. Also find the equation of the line parallel to it and crossing the <\/strong>axis at a distance of 2 units below the origin.<\/strong><\/p>\n

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

Equation of the line passing through point (0, 2) having slope is<\/p>\n

<\/p>\n

<\/p>\n

Now the line parallel to this line having slope and <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

15. The perpendicular from the origin to a line meets it at the point <\/strong> find the equation of the line.<\/strong><\/p>\n

Ans. <\/strong>Here, Slope of the line OP = <\/p>\n

Since the required line is perpendicular to OP.<\/p>\n

<\/p>\n

Slope of required line = <\/p>\n

Equation of the required line is<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

16. The length L (in centimeter) of a copper rod is a linear function of its Celsius temperature C. In an experiment if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C.<\/strong><\/p>\n

Ans. <\/strong>Let the length be represented by and the temperature by <\/p>\n

= (20, 124.943) and = (110, 125.134)<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

17. The owner of a milk store finds that he can sell 980 liters of milk each week at Rs. 14 litre and 1220 liters of milk each week at Rs. 16 liters. Assuming a linear relationship between selling price and demand, how many liters could he sell weekly at Rs. 17 liter?<\/strong><\/p>\n

Ans. <\/strong>Here, = (980, 14) and = (1220, 16)<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Putting we have<\/p>\n

<\/p>\n

<\/p>\n

liters<\/p>\n

\n

18. P<\/strong> is the mid-point of a line segment between axis. Show that equation of the line is <\/strong><\/p>\n

Ans. <\/strong>Let A and B be two points where the line intersect and axis respectively and P is mid-point of AB.<\/p>\n

<\/p>\n

Then <\/p>\n

<\/p>\n

And <\/p>\n

<\/p>\n

Equation of the required line is<\/p>\n

<\/p>\n

<\/p>\n

\n

19. Point R<\/strong> divides a line segment between the axis in the ratio 1: 2. Find equation of the line.<\/strong><\/p>\n

Ans. <\/strong>Let A and B be two points where the line intersect and axis respectively and R is a point divides AB in the ratio 1: 2.<\/p>\n

<\/p>\n

and <\/p>\n

and <\/p>\n

Equation of the required line is<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

\n

20. By using concept of equation of a line, prove that the three points (3, 0), <\/strong> and (8, 2) are collinear.<\/strong><\/p>\n

Ans. <\/strong>Here, = (3, 0) and = <\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Putting the coordinates of third point, we have <\/p>\n

16 \u2013 10 = 6<\/p>\n

6 = 6<\/p>\n

Therefore, third point lies on the line of first two points and given three points are collinear.<\/p>\n","protected":false},"excerpt":{"rendered":"

Exercise 10.2 In Exercises 1 to 8, find the equations of the line which satisfy the given conditions: 1. Write the equations for the and axis. Ans. Equation for axis is Equation for axis is 2. Passing through the point with slope Ans. Given: and 3. Passing through (0, 0) with slope Ans. Given: and … 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-4614","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions"],"yoast_head":"\nNCERT Solutions class-11 Maths Exercise 10.2 | 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-10-2\/\" \/>\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 10.2 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Exercise 10.2 In Exercises 1 to 8, find the equations of the line which satisfy the given conditions: 1. 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