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AP EAMCET202021 Sep 2020Morning ShiftMathematicsStraight LinesActual

The locus of the point whose ratio of distance from the origin to its distance from ((-2,-3) ) is (5: 7 ), is given by.........

Options

  1. A(24 (x^2+y^2 )-100 x-150 y-325=0 )
  2. B(24 (x^2+y^2 )+100 x+150 y-325=0 )
  3. C(24 (x^2+y^2 )-100 x+150 y+325=0 )
  4. D(2 x^2+2 y^2=325 )

Correct answer

A. (24 (x^2+y^2 )-100 x-150 y-325=0 )

Step-by-step solution

Let the point (P(x, y) ), such that (O P: A P=5: 7 ), where (O ) is the origin and (A(-2,-3) ), so ( aligned & x^2+y^2 (x+2)^2+(y+3)^2 = 5 7 & 49 (x^2+y^2 )=25 [x^2+y^2+4 x+6 y+13 ] & 24 (x^2+y^2 )-100 x-150 y-375=0 aligned ) Hence, option (a) is correct.

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