CBSE Class 11 Mathematics Straight Lines Assignment Set A

Multiple Choice Questions

Question. Transform the equation of the line 3x + 2y − 7 = 0 to slope intercept form then the slope and y-intercept will be
(a) 3/2, 7/2
(b) − 3/2 - 7/2
(c) − (3/2, 7/2)
(d) None of these
Answer : C

Question. Transform the equation of the line 3x + 2y − 7 = 0 to normal form then the inclination of the perpendicular segment from the origin on the line with the axis and its length is
(a) tan^-1 (1/3) 7/√13
(b) tan^-1 (2/3) 7/√13
(c) tan^-1 (3/4) 7/√13
(d) tan^-1 (1/5) 7/√13
Answer : B

Question. If the line x/a + y/b = 1 passes through the points (2, −3) and (4, −5), then (a, b) is
(a) (1, 1)
(b) (−1, 1)
(c) (1, −1 )
(d) (−1, −1)
Answer : D

Question. The distance between the parallel lines 3x − 4y + 7 = 0 and 3x − 4y + 5 = 0, is
(a) 3/7
(b) 7/5
(c) 2/5
(d) 3/5
Answer : C

Question. The angle between the lines y − √3x − 5 = 0 and √3y − x + 6 = 0 will not be
(a) 30°
(b) 150°
(c) 45°
(d) None of these
Answer : C

Question. Lines through the points (−2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24).
Then, the value of x is
(a) 2
(b) 6
(c) 8
(d) 4
Answer : D

Question. The perpendicular distance from origin to the line 5x + 12y − 13 = 0 is
(a) 10 unit
(b) 5 unit
(c) 2 unit
(d) 1 unit
Answer : D

Question. The angle between the lines x − 2y + 3 = 0 and 3x + y − 1 = 0 is
(a) − tan⁻¹(7)
(b) tan⁻¹(1/7)
(c) π − tan⁻¹(7)
(d) 2π − tan⁻¹(7)
Answer : C

Question. The equation of line, which passes through point (4, 3) and parallel to the line 2x − 3y = 7 is
(a) 2x − 3y + 1 = 0
(b) 2x − 3y −1 = 0
(c) 2x + 3y + 1 = 0
(d) 2x + 3y −1 = 0
Answer : A

Question. The distance between the lines 3x + 4y = 9 and 6x + 8y = 15 is
(a) 3/10
(b) 2/25
(c) 7/10
(d) 3/25
Answer : A

Question. The distance of the point (3, − 5) from the line 3x − 4y − 26 = 0 is
(a) 3/7
(b) 2/5
(c) 7/5
(d) 3/5
Answer : D

Case Based MCQs

Three girls, Rani, Mansi, Sneha are talking to each other while maintaining a social distance due to covid-19. They are standing on vertices of a triangle, whose coordinates are given.

Based on the above information answer the following questions.

Question. The equation of lines formed by Rani and Mansi is
(a) 3x − y = 4
(b) 3x + y = 4
(c) x − 3y = 4
(d) x + 3y = 4
Answer : B

Question. Slope of equation of line formed by Rani and Sneha is
(a) 2/3 
(b) − 3/2
(c) −2/3
(d) 1/3
Answer : C

Question. The equation of median of lines through Rani is
(a) 5x + 4y = 2
(b) 5x −4y = 2
(c) 4x −5y = 1
(d) None of these
Answer : A

Question. The equation of altitude through Mansi is
(a) 3x −2y = 1
(b) 2x + 3y = 5
(c) x + 2y = 3
(d) None of these
Answer : A

Question. The equation of line passing through the Rani and parallel to line formed by Mansi and Sneha is
(a) x −2y = 4
(b) x + 2y = 6
(c) x −2y = 6
(d) 2x + y = 4
Answer : C

Consider the DABC with vertices A(1, 4), B (2, − 3) andC(− 1, − 2) as shown in the given figure. AD is the median and AM is the altitude through A.

Based on the above information answer the following questions.

Question. Find the distance between A andC
(a) √40 units
(b) √53 units
(c) √41 units
(d) √29 units
Answer : A

Question. Find the slope of BC.
(a) −(4/3)
(b) −(1/3)
(c) −(3/2)
(d) −(3/4)
Answer : B

Question. Find the equation of median through A.
(a) x −13y + 9 = 0
(b) x + 13y −9 = 0
(c) 13x − y −9 = 0
(d) 2x −13y + 9 = 0
Answer : C

Question. Find the equation of the altitude through A.
(a) 3x − y + 1 = 0
(b) x + 2y − 3 = 0
(c) x − 3y + 2 = 0
(d) 3x + 2y −2 = 0
Answer : A

Question. Find the equation of right bisector of side BC.
(a) x + 3y − 3 = 0
(b) x − 3y + 3 = 0
(c) 3x − y −4 = 0
(d) 3x + y −2 = 0
Answer : C

Q1. Find the slope of the lines which makes the following angles with the positive direction of x axis: (i) 2π/3(ii) –π/4

Q2. State the relation between the lines passing through the points

(i) (5,6);(2,3) and (9,-2);(6,-5)

(ii) (3, 15) ; (16,6) and (-5,3);(8,2).

Q3. Prove that the points (-4,-1) ,(-2,4),(4,0) and (2,3) are the vertices of a rectangle.

Q4. If three points (h, 0); (a, b) and (0,k) lie on a line, show that : a/h + b/k = 1.

Q5. Find the equation of a line parallel to x axis and passing through the point (3,-5).

Q6. Find the equation of a line equidistant from the lines x= -2 and x = 6.

Q7. Find the equation of the line with slope -1 and cutting off an intercept of 4 units on negative direction of y-axis.

Q8. Find the equation of the perpendicular bisector of the line segment joining the points (2, 3) and (6, -5).

Q9. Find the equation of the straight line passing through (3,-2) and making an angle of 60˚ with the positive direction of x axis.

Q10. Find the ratio in which the line segment joining the points (2, 3) and (4, 1) divides the line segment joining the points (1, 2) and (4,3).

Q11. Find the equations of the medians of the triangle, the coordinates of whose vertices are (-1, 6) ;(-3, -9) and (5 , -8).

Q12. Find the equation of the line which cut off intercepts on the axes such that their sum and product are 1 and -6 respectively.

Q13. Find the equation of the straight line which is at a distance of 3√2 units from the origin and the perpendicular from the origin makes an angle of 75˚ with the positive direction of x axis.

Q14. Transform the following equations of the line to (i) slope intercept form and find its slope and y intercept

(ii) intercept form and find intercepts on the coordinate axes

(iii) normal form and find the inclination and length of the perpendicular:

a) √3 x + y – 8 = 0

b) 3x – 4y + 4 = 0

c) 4x – 3y + 12 = 0

d) x + √3 y – 4 = 0

e) 5x – 12y +26 = 0

Q15. Find the value of ‘k’ for which the line (k – 3) x – (4 – k²)y + k² - 7k + 6 = 0 is parallel to y axis.

Q16. Find the equation of a line that passes through the intersection of 4x +3y =6, and 3x +4y =8 and whose slope is 1.
Answer : x-y +2 =0

Q17. Find the equation of the line passing through the midpoint of the line segment joining the point (1,3) and (2,-1) and parallel to the line 3x-y =7
Answer : 6x-2y =7,

Q18. Find the equation of the line passing through the midpoint of the line segment joining the point (3,4) and (5,-2) and perpendicular to the line x+3y =8
Answer : 3x-y =11,

Q19. Find what the equation x2+xy-3y2-y+2=0 becomes when the origin is shifted to the point (1,1)
Answer : X²-3Y²+XY+3X-6Y=0

Q20. Find the equations of the medians of the triangle ABC whose vertices are A (2, 5), B (-4, 9) and C (-2,-1)
Answer : 8x-y+15=0, x-5y+23=0, 7x+4y-8=0

Q21. Find the image of the point (-8, 12) with respect to the line mirror 4x+7y+13 = 0.
Answer : (-16,-2)

Q22. Find the equation of the line passing through the intersection of the lines 3x-4y+1 = 0 and 5x+y-1 = 0 and cutting off equal intercepts on the coordinate axes.
Answer : 23x+23y=11

Q23. Find the coordinates of the foot of the perpendicular from a point (-1, 3) to the line3x-4y=16
Answer : 68/25,-49/25)

Q24. Find the equation of the line parallel to y- axis and drawn through the point of intersection of x-7y+5=0 and 3x+7y=7
Answer : x = 1/2

Q25. Find the equation of parabola with focus at (5, 0) and directrix x+5=0, Also find the length of latus rectum.
Answer : y² =20x, 20

Q26. For the parabola y2=-12x, Find the coordinates of focus, the equation of directrix and length of latus rectum.
Answer : (-3, 0), x=3, 12

Q27. Find the equation of parabola with vertex at origin and having directrix y = 2
Answer : x²=-8y

Q28. Find the equation of the circle which passes through the points (5,-8), (2,-9) and (2, 1). Find also the coordinate of its centre and radius.
Answer : x²+y²-4x +8y-5=0, (2,-4), 5,

Q29. Find the equation of the circle which passes through the points (-2,-3) and has its centre on negative side of x-axis and is of radius 5 units.
Answer : x²+y²+12x +11=0,

Q30. Find the equation of the circle whose centre is (3,-2) and which passes through the intersection of the line 5x +7 y = 3 and 2x-3y = 7,
Answer : x²+y²-6x +4y+11=0,

Q31. Find the equation of the circle which passes through the points (3,-2), (-2, 0) and having the line segment 2x-y=3 as its diameter.
Answer : x²+y²+3x +12y+2=0,

Q32. Find the equation of the circle which passes through the points (-3, 1), (6, 4) and (2, -6).
Answer : 13x²+13y²-64x +10y-332=0,

Please click the below link to access CBSE Class 11 Mathematics Straight Lines Assignment Set A