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AP EAMCET202021 Sep 2020Morning ShiftMathematicsStraight LinesActual

The locus of a point (P ) such that (P A+P B=4 ) where (A(2,3,4), B(-2,3,4) ) is

Options

  1. A(y^2+z^2+6 y+8 z+25=0 )
  2. B(y^2-z^2+6 y+8 z-25=0 )
  3. C(y^2+z^2-6 y-8 z+25=0 )
  4. D(y^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 points are (A(2,3,4) ) and (B(-2,3,4) ) and (A B=4 ). Now let point (P(x, y, z) ), such that (P A+P B=4=A B ) means point (P ) is collinear with points (A ) and (B ) and lies between them, so ( array ll & x-2 2+2 = y-3 3-3 = z-4 4-4 & y-3=0=z-4 or & (y-3)^2+(z-4)^2=0 & y^2+z^2-6 y-8 z+25=0 array ) Hence, option (c) is correct.

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