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MHT-CET Pair of Straight Lines — practice questions

Explore 29 free Pair of Straight Lines questions in MHT-CET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Pair of Straight Lines questions and exercises with answers

Showing questions 1–29 of 29.

What is the combined equation of the lines 2x + 3y = 0 and x - 2y = 0?Read the answer and worked solution →The lines x + y = 0 and x - y = 0 have which combined equation?Read the answer and worked solution →Which equation represents the two coordinate axes together?Read the answer and worked solution →Which pair of separate lines is given by x² - 5xy + 6y² = 0?Read the answer and worked solution →What is the degree of the term 3xy in an algebraic expression?Read the answer and worked solution →What is the degree of a non-zero constant term such as 2?Read the answer and worked solution →Which of these is a homogeneous equation?Read the answer and worked solution →Why is 3x² + 2xy + 2y² + 5x = 0 not a homogeneous equation?Read the answer and worked solution →Which is the general form of a homogeneous equation of degree two in x and y?Read the answer and worked solution →Two lines through the origin have a joint equation that is always of which type?Read the answer and worked solution →A homogeneous equation ax² + 2hxy + by² = 0 represents a pair of real lines through the origin whenRead the answer and worked solution →For ax² + 2hxy + by² = 0, the two lines coincide exactly whenRead the answer and worked solution →The lines given by ax² + 2hxy + by² = 0 are perpendicular if and only ifRead the answer and worked solution →Which equation gives two mutually perpendicular lines?Read the answer and worked solution →What are the slopes of the lines x² - 2xy - 3y² = 0?Read the answer and worked solution →The auxiliary equation whose roots are the slopes of ax² + 2hxy + by² = 0 isRead the answer and worked solution →In ax² + 2hxy = 0 (b = 0), one of the two lines isRead the answer and worked solution →The lines xy = 0 make what angle with each other?Read the answer and worked solution →For what value of k are the lines kx² + 4xy - 3y² = 0 perpendicular?Read the answer and worked solution →The lines 4x² - 4xy + ky² = 0 are coincident when k equalsRead the answer and worked solution →For x² - 6xy + 5y² + 10x - 14y + 9 = 0, what is abc + 2fgh - af² - bg² - ch²?Read the answer and worked solution →Find tan θ for the acute angle between the pair x² - 6xy + 5y² + 10x - 14y + 9 = 0.Read the answer and worked solution →Where do the lines in x² - 6xy + 5y² + 10x - 14y + 9 = 0 intersect?Read the answer and worked solution →What is the joint equation of the bisectors of the angles between ax² + 2hxy + by² = 0?Read the answer and worked solution →What is the relation between the two angle bisectors of a pair of lines through the origin?Read the answer and worked solution →Find the bisector pair for the lines 3x² + 10xy + 3y² = 0.Read the answer and worked solution →What does the equation uv = 0 represent, where u = 0 and v = 0 are lines?Read the answer and worked solution →An equation that represents two lines at once is called what?Read the answer and worked solution →If m1 and m2 are slopes of the lines of ax² + 2hxy + by² = 0, then m1m2 equalsRead the answer and worked solution →

Worked practice questions

What is the combined equation of the lines 2x + 3y = 0 and x - 2y = 0?

  1. 2x² - xy - 6y² = 0
  2. 2x² + xy - 6y² = 0
  3. 2x² - xy + 6y² = 0
  4. 2x² - 7xy - 6y² = 0
Show answer and solution

Correct answer: A. 2x² - xy - 6y² = 0

Multiplying (2x + 3y)(x - 2y) gives 2x² - 4xy + 3xy - 6y², which is 2x² - xy - 6y².

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The lines x + y = 0 and x - y = 0 have which combined equation?

  1. x² - y² = 0
  2. xy = 0
  3. x² + y² = 0
  4. x² + xy = 0
Show answer and solution

Correct answer: A. x² - y² = 0

The product (x + y)(x - y) expands to x² - y², set equal to zero.

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Which equation represents the two coordinate axes together?

  1. xy = 0
  2. x + y = 0
  3. x² + y² = 0
  4. x² - y² = 0
Show answer and solution

Correct answer: A. xy = 0

The axes are x = 0 and y = 0, so their product gives xy = 0.

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More Mathematics topics

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