Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202520 Apr 2025Morning ShiftMathematicsPair of LinesActual

The distance between the lines represented by the equation 4 x^2+4 x y+y^2-6 x-3 y-4=0 is

Options

  1. A1 5 units
  2. B1 5 units
  3. C5 units
  4. D5 units

Correct answer

C. 5 units

Step-by-step solution

The quadratic 4x^2 + 4xy + y^2 is a perfect square, factoring as (2x + y)^2 . This substitution reduces the original equation 4x^2 + 4xy + y^2 - 6x - 3y - 4 = 0 to (2x + y)^2 - 3(2x + y) - 4 = 0 . Letting Y = 2x + y gives the quadratic Y^2 - 3Y - 4 = 0 , which factors as (Y - 4)(Y + 1) = 0 . The solutions are Y = 4 and Y = -1 . Substituting back produces the two parallel lines: 2x + y - 4 = 0 2x + y + 1 = 0 The distance between parallel lines of the form Ax + By + C₁ = 0 and Ax + By + C₂ = 0 is given by d = |C₁ - C

Practice Pair of Lines on Quantrex Academy →

More from Pair of Lines

If the angle made by the lines represented by the equation ax^2 + 2hxy + by^2 = 0 with X-axis are and , then ( + ) is 2026If the equation 16x^2 - 24xy + 9y^2 - 8x + 6y - 35 = 0 represents a pair of straight lines, then the equation of the locus of points equidistant from these two lines is.......... 2026If two lines represented by x^2 - (1 + 3 )xy + 3 y^2 = 0 make angles and with the X-axis, then ( + ) is... 2026If the combined equation of angle bisectors of the lines x^2 - 2pxy - y^2 = 0 is x^2 - 2qxy - y^2 = 0 , then which of the following is true? 2026The combined equation of lines parallel to the coordinate axes and passing through the point of intersection of lines represented by x^2 - 6xy + 5y^2 + 10x - 14y + 9 = 0 is 2026Two lines are given by x^2 - 4xy + 4y^2 + kx - 2ky = 0 , then the value of k so that the distance between them is 3 is 2026If the equation ax^2 + 4xy - 2y^2 + 4x + 8y + 1 = 0 represents a pair of straight lines, then the coordinates of their point of intersection are......... 2026The joint equation of a pair of lines passing through point (1,4) , one of which is parallel to X-axis and the other makes an angle of 45^ with the positive direction of X-axis, is 2026 Full Pair of Lines list All MHT CET PYQs