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AP EAMCET202420 May 2024Evening ShiftMathematicsStraight LinesActual

A(2,3), B(-1,1) are two points. If P is a variable point such that A P B=90^ then locus of P is

Options

  1. Ax^2+y^2-x-4 y+1=0
  2. Bx^2+y^2+x+4 y-1=0
  3. Cx^2+y^2-x+4 y-1=0
  4. Dx^2+y^2+x-4 y+1=0

Correct answer

A. x^2+y^2-x-4 y+1=0

Step-by-step solution

A (2,3), B (-1,1) and APB =90^ Using Pythagoras theorem aligned & AB ^2= AP ^2+ BP ^2 & (2+1)^2+(3-1)^2=(x-2)^2+(y-3)^2+(x+1)^2 & +(y-1)^2 & 13=2 x^2+2 y^2-2 x-8 y+15 & x^2+y^2-x-4 y+1=0 aligned

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