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AP EAMCET2015MathematicsStraight Lines

If the equation to the locus of points equidistant from the points (-2,3),(6,-5) is a x+b y+c=0 , where a>0 , then the ascending order of a, b, c is

Options

  1. Aa,b,c
  2. Bc,b,a
  3. Cb,c,a
  4. Da,c,b

Correct answer

B. c,b,a

Step-by-step solution

Let P(x, y) be the required point whose locus is given by a x+b y+c=0 Also given that P is equidistant from A(-2,3) and B(6,-5) . Then, aligned & P A=P B or P A^2=P B^2 & (x+2)^2+(y-3)^2=(x-6)^2+(y+5)^2 & x^2+4 x+4+y^2-6 y+9 & =x^2-12 x+36+y^2+10 y+25 & 16 x-16 y-48=0 & x-y-3=0 aligned On comparing with a x+b y+c=0 , we get a=1, b=-1, c=-3 Hence, the ascending order is c, b, a .

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