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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

Line L has intercepts a and b on the coordinate axes, when the axes are rotated through a given angle keeping the origin fixed, the same line has intercepts p and q, then

Options

  1. Aa 2 + b 2 = p 2 + q 2
  2. B1 a 2 + 1 b 2 = 1 p 2 + 1 q 2
  3. Ca 2 + p 2 = b 2 + q 2
  4. D1 a 2 + 1 p 2 = 1 b 2 + 1 q 2

Correct answer

B. 1 a 2 + 1 b 2 = 1 p 2 + 1 q 2

Step-by-step solution

Equation of L is x a + y b = 1 and its distance from the origin is 1 1 a 2 + 1 b 2 Let the axis be rotated through an angle θ and let X, Y be the new coordinates of any point P x, y in the plane, then new equation of L will be X p + Y q = 1 and its distance from the origin is 1 1 p 2 + 1 q 2 As the origin is fixed, distance from origin will be same in both cases 1 a 2 + 1 b 2 = 1 p 2 + 1 q 2

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