Unit 4: Pair of Straight Lines — Online MCQ Test
MATHEMATICS - 1B · CLASS 11 INTERMEDIATE 1 YEAR · Telangana State Board
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This chapter covers: This chapter covers homogeneous second-degree equations pair of lines passing through origin angle between lines bisectors of angles and condition for general second-degree equatio....
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Unit 4: Pair of Straight Lines — Important Questions & Answers
A homogeneous second-degree equation in x and y represents a pair of straight lines passing through the ______.
- A. origin
- B. point (1,1)
- C. x-axis
- D. y-axis
Answer: A. origin
A homogeneous equation of degree 2 has all terms of the same degree and represents lines passing through the origin.
A homogeneous equation of degree 2 has all terms of the same degree and represents lines passing through the origin.
The equation representing two straight lines through the origin is generally of the form:
- A. ax + by + c = 0
- B. ax^2 + 2hxy + by^2 = 0
- C. x^2 + y^2 = 1
- D. x^2 + y^2 + 2gx + 2fy + c = 0
Answer: B. ax^2 + 2hxy + by^2 = 0
A pair of lines through the origin is represented by a homogeneous quadratic equation in x and y.
A pair of lines through the origin is represented by a homogeneous quadratic equation in x and y.
Which of the following is NOT a homogeneous second-degree equation?
- A. x^2 + 2xy + y^2 = 0
- B. x^2 - y^2 = 0
- C. 3x^2 + 5xy - 2y^2 = 0
- D. x^2 + y^2 + x = 0
Answer: D. x^2 + y^2 + x = 0
A homogeneous second-degree equation must contain only terms of degree 2. The term x makes option D non-homogeneous.
A homogeneous second-degree equation must contain only terms of degree 2. The term x makes option D non-homogeneous.
If the pair of lines represented by x^2 + 2hxy + y^2 = 0 are equally inclined to the x-axis in opposite directions, then the angle between them is:
- A. 30°
- B. 45°
- C. 60°
- D. 90°
Answer: D. 90°
Lines equally inclined to the x-axis in opposite directions are symmetric about an axis, and in this homogeneous pair the relevant case is perpendicular when the coefficient of x^2 and y^2 are equal and opposite conditions lead to 90°.
Lines equally inclined to the x-axis in opposite directions are symmetric about an axis, and in this homogeneous pair the relevant case is perpendicular when the coefficient of x^2 and y^2 are equal and opposite conditions lead to 90°.
For the equation x^2 - 2xy + y^2 = 0, which of the following is the correct pair of lines?
- A. x = y and x = -y
- B. x = 0 and y = 0
- C. x = y only
- D. x = 2y and x = -2y
Answer: C. x = y only
x^2 - 2xy + y^2 = (x - y)^2 = 0, so it represents the same line x = y twice.
x^2 - 2xy + y^2 = (x - y)^2 = 0, so it represents the same line x = y twice.