advertisement

AHLCON PUBLIC SCHOOL Class : XI - MATHEMATICS Assignment – 10 (2014 – 2015) Chapter : Straight Lines Questions: 1. Find the equation of the line which satisfies the given conditions. a. Passing through the point 1,2 with slope 4. 2 ,2 2, with slope 2 3 . c. Passing through the point 2,2 and inclined to x – axis at 45o. b. Passing through the point d. Intersecting x – axis at a distance of 4 units to the right of origin with slope – 1. e. Passing through the points 0,3 and 5,0 . 2. Find the equation of the right bisectors of the line segment joining the points A1,0 and B2,3 . 3. Find the equations of medians of triangle ABC whose vertices are A 1,6 , B 3,9 , C5,8 . 4. Find the equations of the sides of the triangle whose vertices are 2,1, 2,3, 4,3. 5. The points A1,3 and C 6,8 are the two opposite vertices of the square ABCD. Find the equations of the diagonal BD. 6. ABCD is a rectangle. The points A and C are 3,1 and 1,1 respectively. Equation AB is 4 x 7 y 5 0 . Find the equation of other three sides. 7. The base of an equilateral triangle is x – axis and the vertex is 0,4 . Find the equation of other two sides. 8. The area of the triangle formed by co-ordinate axes and a line is 6 sq. units and the length of hypotenuse is 54m. Find the equation of the line. 9. Find the equation of a line which passes through 12,2 and is such that the intercept on x – axis exceeds the intercept on y – axis by 4 units. 10. Reduce the following equations into slope intercept form: a) 3 x 3 y 5 b) 7 x 3 y 6 0 11. Reduce each of the following to the normal form and find the length of perpendicular from origin to the line. 1. 2. x y20 4x 3y 9 0 12. Reduce the following equations to intercept form and find the intercepts on the axes. i. ii. 3x y 2 0 3 x 4 y 12 13. Find the coordinates of the ortho-centre of the triangle whose vertices are 1,3, 2,3 and 0,0 . 14. Find the angle between the lines y 3 x 5 0 and 3y x 6 0 . 15. A vertex of an equilateral triangle is 2,3 and the equation of the opposite side is the equation of other two sides. 3 x y 2. Find 16. Determine the distance between pair of lines in each case. a) 4 x 3 y 9 0 and 4 x 3 y 24 0 b) 9 x 40 y 20 and 9 x 40 y 103 0 17. Find the equations of the lines which pass to the point 4,5 and made equal angles with the lines 5 x 12 y 6 0 and 3 x 4 y 7 . 18. Two lines cut the x – axis at distances 4 and -4 and the y – axis at distances 2 and 6 respectively from the origin. Find the co-ordinates of their point of intersection. 19. A lines forms a triangle with co-ordinate axis. If the area of the triangle is 54 3 square units and perpendicular drawn from the origin to the line makes an angle of 60 degree with x – axis. Find the equation of the line. 20. Prove that the diagonals of the parallelogram formed by the lines 3 x y 0, 3 y x 0, 3 x y 1, 3 y x 1 are at right angle to each other. 21. Find the equation of the line through the intersection of 5 x 3 y 1 and 2 x 3 y 23 0 and perpendicular to the line 5 x 3 y 1 0 . 22. Find the equation of the line through the intersection of x 2 y 3 0 and 4 x y 7 0 and which is parallel to 5 x 4 y 20 0 23. The points 1,3 and 5,1 are the opposite vertices of rectangle. The other two vertices lie on y 2 x c . Find the c and the other vertices. 24. Find the equation of the line through the point 3,2 which makes an angle of 45degree with x 2y 3. 25. One side of a square is inclined to the x – axis at an angle and one of the extremities is at the origin. If the side of square is 4 find the equation of the diagonals of the square. 26. Find the point on the line x 2 y 3 whose distance from 3x 4 y 2 0 is 2. 27. A ray of light passing through the point 4,5 and reflects on the x – axis at a point 3,0 . Find the equation of the reflected ray. 28. Prove that the line 5 x 2 y 1 0 is mid parallel to the lines 5 x 2 y 9 0 and 5 x 2 y 7 0 . 29. If the origin be shifted to the point 2,3 by a transaction of coordinate axes. Find the new coordinates of point 4,7 . 30. If the origin be shifted to the point 3,1 . Find the new equation of the line 2 x 3 y 5 0 31. Find the point to which the origin be shifted after a translation, so that the equation x 2 y 2 4 x 8 y 3 0 will have no first degree form. 32. Transform the equations 2 x 2 y 2 4 x 4 y 0 to parallel axes when the origin is shifted to the point 1,2