Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202611 April 2026Morning ShiftMathematicsPair of LinesActual

If the equation x^2 - ky^2 - 4x + 6y - 5 = 0 represents a pair of straight lines, then their point of intersection is

Options

  1. A(1, 2)
  2. B(2, 3)
  3. C(3, 4)
  4. D(4, 5)

Correct answer

B. (2, 3)

Step-by-step solution

The given equation is x^2 - ky^2 - 4x + 6y - 5 = 0 . Comparing this with the general second-degree equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 , we get: a = 1 , h = 0 , b = -k , g = -2 , f = 3 , c = -5 . For the equation to represent a pair of straight lines, the condition is abc + 2fgh - af^2 - bg^2 - ch^2 = 0 . Substituting the values: (1)(-k)(-5) + 0 - (1)(3)^2 - (-k)(-2)^2 - 0 = 0 5k - 9 + 4k = 0 9k = 9 k = 1 So, the equation of the pair of straight lines is x^2 - y^2 - 4x + 6y - 5 = 0 . Let F(x, y) = x^2 -

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