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AP EAMCET202420 May 2024Morning ShiftMathematicsStraight LinesActual

If the line segment joining the points (1,0) and (0,1) subtends an angle of 45^ at a variable point P , then the equation of the locus of P is

Options

  1. A(x^2+y^2-1 ) (x^2+y^2-2 x-2 y+1 )=0, x 0,1
  2. B(x^2+y^2-1 ) (x^2+y^2+2 x+2 y+1 )=0, x 0,1
  3. Cx^2+y^2+2 x+2 y+1=0
  4. Dx^2+y^2=4

Correct answer

A. (x^2+y^2-1 ) (x^2+y^2-2 x-2 y+1 )=0, x 0,1

Step-by-step solution

Slope of AP = k h-1 Slope of BP = k-1 h = , m₁-m₂ 1+m₁ m₂ 45^ = | k h-1 - k-1 h 1+ k(k-1) h(h-1) | 1= | k h-(h-1)(k-1) h(h-1)+k(k-1) | h^2-h+k^2-k=k h-k h+h+k-1 h^2+k^2-2 h-2 k+1=0 Locus is x^2+y^2-2 x-2 y+1=0 (1,0) and (0,1) satisfy x^2+y^2-1=0 Locus is (x^2+y^2-1 ) (x^2+y^2-2 x-2 y+1 )=0

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