ASSIGNMENTS AT TUTORBREEZE.COM. Mathematics Class 11. Write to me at
for more information on live online tutoring in ...
ASSIGNMENTS AT TUTORBREEZE.COM Mathematics Class 11 Write to me at
[email protected] for more information on live online tutoring in Mathematics, Physics, Chemistry for students of Classes 5-12 at TutorBreeze.com. Study from the Best Teachers to get the Best Result! ____________________________________________________________________________________________________________
1.
Straight Lines Find the equation of the line parallel to the y-axis and 3 units to the right of it. Determine the equation of the line parallel to the x-axis and
2.
has intercept on the y-axis as −2 . In questions 3 and 4, find the equation of the line, which satisfies the given conditions:
3.
Passing through ( 2,2) and inclined to x-axis at 450.
4.
Intersecting the y-axis at a distance of 2 units above the origin and making an angle of 300 with positive direction of x-axis. π 2π and with the x-axis. Find the lines through the point ( 0,2) making angles 3 3 Also find the lines parallel to them cutting the y-axis at a distance of 2 units below the origin. Find the equation of the right bisector of the line segment joining the points A (1,0 ) and B ( 2,3 ) .
5.
6. 7.
Find the equation of the line passing through ( −3,5 ) and perpendicular to the line through the points ( 2,5 ) and ( −3, 6 ) .
8.
9.
10.
Determine the equation of the line, which cuts off an intercept −5 on y-axis and 1 having slope . 2 If p be the measure of the perpendicular segment from the origin to the line 1 1 1 whose intercept on the axes are a and b, show that 2 = 2 + 2 . p a b Find the equation of the line where the perpendicular distance of the origin from the line, p and the angle made by the perpendicular, ω are given:
p = 5, ω = 300 p = 5, ω = 1350
11. 12.
Find the equation of the line through ( −2,1) in symmetrical form when the angle made by the line with positive direction of x-axis is 450.
13. Reduce the following equation to slope–intercept form 6x + 3y − 5 = 0 14. Reduce the normal form and find the length of the perpendicular from the origin to the line. (i) x − 4 = 0
( ii ) 4x + 3y − 9 = 0 15. Find the coordinates of the foot of the perpendicular from a point ( −1,3 ) to the line 3x − 4y − 16 = 0 16. Find the coordinates of the orthocentre of the triangle whose vertices are ( −1,3 ) , ( 2, −1) and ( 0,0 ) 17. The line through ( 4,3 ) and ( −6,0 ) intersects the line 5x + y = 0. Find the angles of intersection.
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ASSIGNMENTS AT TUTORBREEZE.COM Mathematics Class 11 Write to me at
[email protected] for more information on live online tutoring in Mathematics, Physics, Chemistry for students of Classes 5-12 at TutorBreeze.com. Study from the Best Teachers to get the Best Result! ____________________________________________________________________________________________________________
18. Find the equations of the lines that pass through the point ( 4,5 ) and make equal angles with the lines 5x − 12y + 6 = 0 and 3x = 4y + 7 19. Determine the distance between the following pair of parallel lines: 4x − 3y − 9 = 0 and 4x − 3y − 24 = 0 20. Find the length of the perpendicular from the origin to the line joining two points whose coordinates are ( cos θ, sinθ ) and ( cos φ, sinφ ) 21. Find the equations of the bisectors of the angles formed by the following pair of lines x + y 3 = 6 + 2 3 and x − y 3 = 6 − 2 3 22. Find the equations of the bisectors of the internal angles of a triangle, the equations of whose sides are given below: 3x + 5y = 15; x + y = 4 and 2x + y = 6 23. Find the equation of the straight line drawn perpendicular to the line
x y + =1 a b
through the point where it meets the y-axis. 24. Find the equation of the straight line passing through the intersection of the lines 4x + 7y − 3 = 0 and 2x − 3y + 1 = 0 and have equal intercepts on the axes. 25. One side of a rectangle lies along the line 4x + 7y + 5 = 0. Two of its vertices are
( −3,1)
and (1,1) . Find the equation of the other 3 sides.
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ASSIGNMENTS AT TUTORBREEZE.COM Mathematics Class 11 Write to me at
[email protected] for more information on live online tutoring in Mathematics, Physics, Chemistry for students of Classes 5-12 at TutorBreeze.com. Study from the Best Teachers to get the Best Result! ____________________________________________________________________________________________________________
(ANSWERS) 11. Straight Lines 1. 2.
x=3 y+2=0
3.
x−y=0
4.
x − 3y + 2 3 = 0
5.
3x − y + 2 = 0 and
6.
x + 3y − 6 = 0
7.
5x − y + 20 = 0
8.
x + 2y − 10 = 0
10.
3x − y − 2 = 0,
3x − y + 2 = 0
3x + y = 10
11. y − x = 5 2 12. y − 1 = x + 2 13. -2x+5/3 = y
(i) 14.
x = 4; 4
4 3 9 9 x+ y= ; 5 5 5 5 68 49 15. ,− 25 25 16. ( −4, −3 )
( ii )
53 17. tan−1 − 5 18. 4x − 7y + 19 = 0 and 7x + 4y − 48 = 0 19. 3 units θ−φ 20. cos 2 21. y = 2, x = 6
( (3 −
) ( ) 17 ) x + ( 5 − 17 ) y = 15 − 4 17 and ( 2 2 − 5 ) x + ( 2 − 5 ) y − 6 2 + 4
22. 3 5 − 2 34 x + 5 5 − 34 y − 15 5 + 6 34 = 0
5=0
23. ax − by − b2 = 0 24. 13 ( x + y ) − 6 = 0 25. 4x + 7y − 11 = 0, 7x − 4y − 3 = 0, 7x − 4y + 25 = 0
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