Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202411 May 2024Evening ShiftMathematicsPair of LinesActual

The joint equation of pair of lines through the origin, each of which makes an angle of 30^ with Y -axis, is

Options

  1. A3 x^2-y^2=0
  2. Bx^2-3 y^2=0
  3. C3 x^2+y^2=0
  4. Dx^2+3 y^2=0

Correct answer

A. 3 x^2-y^2=0

Step-by-step solution

Let OA and OB be the required lines. angles made by OA and OB with X -axis are 60^ and 120^ respectively. Their equations are y= 3 x and y=- 3 x i.e., 3 x-y=0 and 3 x+y=0 The joint equation of the lines is ( 3 x-y)( 3 x+y)=0 3 x^2-y^2=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