Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202020 Oct 2020Evening ShiftMathematicsPair of LinesActual

The joint equation of pair of lines through the origin and making equilateral triangle with the line y=4 is

Options

  1. A3 x²+y²=0
  2. B3 x²-y²=0
  3. Cx²-y²=0
  4. Dx²-3 y²=0

Correct answer

B. 3 x²-y²=0

Step-by-step solution

Let L ₁ and L ₂ be the required lines. Since OAB is equilateral, m ABO =60^ = m BAO Slope of line L ₂= 60^ = 3 and Slope of line L₁= ( -60^ )=- 3 Hence required equation is (y- 3 x)(y+ 3 x)=0 i.e. y²-3 x²=0 3 x²-y²=0

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