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AP EAMCET20227 Jul 2022Evening ShiftMathematicsStraight LinesActual

A point P(x, y) is such that the sum of squares of its distance from (a, 0) and (-a, 0) is 2 b^2 . The equation representing the locus of P is

Options

  1. Ax^2+y^2=b^2+a^2
  2. Bx^2+y^2=b^2-a^2
  3. Cx^2+y^2=b^2-2 a^2
  4. Dx^2+y^2=b^2+2 a^2

Correct answer

B. x^2+y^2=b^2-a^2

Step-by-step solution

Let the point be (x, y) . aligned & (x-a)^2+(y-0)^2+(x+a)^2+(y-0)^2=2 b^2 & 2 x^2+2 y^2+2 a^2=2 b^2 & x^2+y^2=b^2-a^2 . aligned

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