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AP EAMCET201825 Apr 2018Morning ShiftMathematicsStraight LinesActual

Let A , B and C be three points in a plane. The locus of a point P moving such that P A 2 + P B 2 = 2 P C 2 is a

Options

  1. Astraight line
  2. Bpair of straight lines
  3. Ccircle
  4. Dparabola

Correct answer

A. straight line

Step-by-step solution

We have A ,   B and C be three points in a plane. Let A ≡ 0 , 1 ,   B ≡ 1 , 0   &   C ≡ - 1 , 0 Let P x , y be any variable point. Then we have P A 2 + P B 2 = 2 P C 2 ⇒ x - 0 2 + y - 1 2 2 + x - 1 2 + y - 0 2 2 = 2 x + 1 2 + y - 0 2 2 ⇒ x 2 + y - 1 2 + x - 1 2 + y 2 = 2 x + 1 2 + y 2 ⇒ 6 x + 2 y = 0 It is a linear equation. Hence, locus of point P x , y is a straight line.

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