Class 11 Mathematics Straight Lines MCQs Set 09

Question. The equation of the pair of lines through the point (a,b) and parallel to the coordinate axes is
(a) \( (x - b)(y - a) = 0 \)
(b) \( (x - a)(y + b) = 0 \)
(c) \( (x - a)(y - b) = 0 \)
(d) \( (x + a)(y - b) = 0 \)
Answer: (c) \( (x - a)(y - b) = 0 \)

Question. If \( ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 \) represents a pair of parallel lines then \( \frac{g^2 - ac}{f^2 - bc} = \)
(a) a/b
(b) \( \sqrt{a/b} \)
(c) b/a
(d) \( \sqrt{b/a} \)
Answer: (b) \( \sqrt{a/b} \)

Question. The distance between the parallel lines \( 9x^2 - 6xy + y^2 + 18x - 6y + 8 = 0 \) is
(a) \( 1/\sqrt{10} \)
(b) \( 2/\sqrt{10} \)
(c) \( 4/\sqrt{10} \)
(d) \( \sqrt{10} \)
Answer: (b) \( 2/\sqrt{10} \)

Question. The distance between the parallel lines \( x^2 + 2\sqrt{2}xy + 2y^2 + 4x + 4\sqrt{2}y + 1 = 0 \) is
(a) 2
(b) \( 2\sqrt{2} \)
(c) \( 4\sqrt{2} \)
(d) 8
Answer: (a) 2

Question. The distance between the two lines represented by \( 8x^2 - 24xy + 18y^2 - 6x + 9y - 5 = 0 \) is
(a) 0
(b) \( \frac{3}{4\sqrt{13}} \)
(c) \( \frac{6}{\sqrt{13}} \)
(d) \( \frac{7}{2\sqrt{13}} \)
Answer: (d) \( \frac{7}{2\sqrt{13}} \)

Question. The product of the perpendicular distances from the point (-2,3) to the lines \( x^2 - y^2 + x + 1 = 0 \) is
(a) 3
(b) 4
(c) 5
(d) 6
Answer: (b) 4

Question. The point of intersection of the straight lines represented by \( 6x^2 + xy - 40y^2 - 35x - 83y + 11 = 0 \)
(a) (3, 1)
(b) (3, -1)
(c) (-3, 1)
(d) (-3, -1)
Answer: (b) (3, -1)

Question. If \( 3x^2 - 11xy + 10y^2 - 7x + 13y + k = 0 \) denotes a pair of straight lines, then the point of intersection of the lines is
(a) (1, 3)
(b) (3, 1)
(c) (-3, 1)
(d) (1, -3)
Answer: (b) (3, 1)

Question. If the equation \( ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 \) represents a pair of straight lines, then the square of the distance of their point of intersection from the origin is
(a) \( \frac{c(a+b) - af^2 - bg^2}{ab - h^2} \)
(b) \( \frac{c(a+b) + f^2 + g^2}{ab - h^2} \)
(c) \( \frac{c(a+b) - f^2 - g^2}{ab - h^2} \)
(d) \( \frac{c(a+b) - f^2 - g^2}{(ab - h^2)^2} \)
Answer: (c) \( \frac{c(a+b) - f^2 - g^2}{ab - h^2} \)

Question. A: The product of the perpendiculars from (2, -1) to the lines \( x^2 + 2xy + y^2 = 0 \)
B: The product of perpendiculars from (1,1) to the pair of lines \( 3x^2 + 10xy + 3y^2 - 28x - 28y + 49 = 0 \)
C: The product of perpendiculars from (0,0) to pair of lines \( 2x^2 - 13xy - 7y^2 + x + 23y - 6 = 0 \)
D: The square of the distance from (0,0) to the point of intersection of \( x^2 - y^2 - x - 3y - 2 = 0 \)
Arrange A,B,C,D in ascending order
(a) D, A, B, C
(b) B, C, A, D
(c) A, B, C, D
(d) C, A, B, D
Answer: (d) C, A, B, D

Question. If the lines \( x^2 + 2xy - 35y^2 - 4x + 44y - 12 = 0 \) and \( 5x + \lambda y - 8 = 0 \) are concurrent, then the value of \( \lambda \) is
(a) 0
(b) 1
(c) -1
(d) 2
Answer: (d) 2

Question. If the pair of lines \( ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 \) intersect on the y-axis, then
(a) \( 2fgh = bg^2 + ch^2 \)
(b) \( bg^2 \neq ch^2 \)
(c) \( abc = 2fgh \)
(d) \( 2fgh = af^2 + ch^2 \)
Answer: (a) \( 2fgh = bg^2 + ch^2 \)

Question. The intercept made by the pair of lines \( 2x^2 + xy - 8y^2 - 2x + 7y + 1 = 0 \) on the Y-axis is
(a) 6
(b) 9/8
(c) 1/5
(d) 5
Answer: (b) 9/8

Question. The figure formed by the pairs of lines \( 2x^2 + 3xy - 2y^2 = 0 \) and \( 2x^2 + 3xy - 2y^2 - 5x + 15y - 25 = 0 \) is a
(a) parallelogram
(b) rhombus
(c) rectangle
(d) square
Answer: (d) square

Question. The pairs of straight lines \( x^2 - 3xy + 2y^2 = 0 \) and \( x^2 - 3xy + 2y^2 + x - 2 = 0 \) form a :
(a) square but not rhombus
(b) rhombus
(c) parallelogram
(d) rectangle but not a square
Answer: (c) parallelogram

Question. A diagonal of the rectangle formed by the lines \( x^2 - 7x + 6 = 0 \) and \( y^2 - 14y + 40 = 0 \) is
(a) 5x+6y=0
(b) 5x-6y=0
(c) 6x-5y+14=0
(d) 6x-5y-14=0
Answer: (c) 6x-5y+14=0

Question. The length of the side of the square formed by the lines \( 2x^2 + 3xy - 2y^2 = 0 \) and \( 2x^2 + 3xy - 2y^2 + 3x + y + 1 = 0 \) is
(a) \( 1/\sqrt{3} \)
(b) \( 1/\sqrt{5} \)
(c) \( 1/\sqrt{7} \)
(d) \( 1/\sqrt{10} \)
Answer: (b) \( 1/\sqrt{5} \)

Question. The angle between the lines joining the origin to the points of intersection of the lines \( \sqrt{3}x + y = 2 \) and the curve \( x^2 + y^2 = 4 \) is
(a) \( \pi/6 \)
(b) \( \pi/4 \)
(c) \( \pi/3 \)
(d) \( \pi/2 \)
Answer: (c) \( \pi/3 \)