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AP EAMCET202316 May 2023Evening ShiftMathematicsStraight LinesActual

If A=(2,3,4) and B=(-2,3,4) , then the locus of a point P such that PA + PB =4 is

Options

  1. Ay^2+z^2+6 y+8 z+25=0
  2. By^2-z^2+6 y+8 z-25=0
  3. Cy^2+z^2-6 y-8 z+25=0
  4. Dy^2+z^2-6 y-8 z-25=0

Correct answer

C. y^2+z^2-6 y-8 z+25=0

Step-by-step solution

Given A=(2,3,4), B=(-2,3,4) aligned & Now, PA +P B=4 P A^2=(4-P B)^2 & (x-2)^2+(y-3)^2+(z-4)^2=16+P^2-8 P B & (x-2)^2+(y-3)^2+(z-4)^2 & =16+(z+2)^2+(y-3)^2+(z-4)^2-8 P B & (x-2)^2=16+(x+2)^2-8 P B & 8 x+16=8 P B 64 P^2=(8 x+16)^2 & 64 ((x+2)^2+(y-3)^2+(z-4)^2 ) & =64 x^2+256+256 x & 64 x^2+64 y^2+64 z^2+256 x-384 y-512 z+1856 & =64 x^2+256+256 x & 64 y^2+64 z^2-384 y-518 z+1856-256=0 & y^2+z^2-6 y-8 z+25=0 aligned

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