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KCET2011MathematicsHyperbola

Locus of a point which moves such that its distance from the x -axis is twice its distance from the line x-y=0 is

Options

  1. Ax²+4 x y-y²=0
  2. B2 x²-4 x y+y²=0
  3. Cx²-4 x y+y²=0
  4. Dx²-4 x y-y²=0

Correct answer

B. 2 x²-4 x y+y²=0

Step-by-step solution

P₁= length of perpendicular from P to x -axis. P₂= length of perpendicular from P to y=x line. aligned P₁ &=2 P₂ |k| &=2 |h-k| 2 aligned Squaring on both sides, k²=2(h-k)² array r k²=2 h²+2 k²-4 h k 2 h²-4 h k+k²=0 array So, the locus of a point P is, 2 x²-4 x y+y²=0

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