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MHT CET202120 Sep 2021Evening ShiftMathematicsPair of LinesActual

The joint equation of pair of lines through the origin and making an equilateral triangle with the line y=3 is

Options

  1. Ax^2+3 y^2=0
  2. B3 x^2-y^2=0
  3. Cx^2+3 y^2=0
  4. D3 x^2+y^2=0

Correct answer

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

Step-by-step solution

Let OAB be the required triangle. Since OAB is an equilateral triangle. Slope of line OA = 60^ = 3 and slope of line OB = 120^ =- 3 Equation of OA is y = 3 x i.e. 3 x - y =0 and equation of O B is y=- 3 x i.e. 3 x + y =0 Hence required joint equation is ( 3 x-y)( 3 x+y)=0 i.e. 3 x^2-y^2=0

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