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AP EAMCET2015MathematicsStraight Lines

The point on the line 4 x-y-2=0 which is equidistant from the points (-5,6) and (3,2) is

Options

  1. A(2,6)
  2. B(4,14)
  3. C(1,2)
  4. D(3,10)

Correct answer

B. (4,14)

Step-by-step solution

Let the required point be P (x₁, y₁ ) and it is on the line 4 x-y-2=0 . Then, Also given, point P is equidistant from A(-5,6) and aligned & B(3,2) . & P A^2=P B^2 & (x₁+5 )^2+ (y₁-6 )^2= (x₁-3 )^2+ (y₁-2 )^2 & x₁^2+10 x₁+25+y₁^2-12 y₁+36 & =x₁^2-6 x₁+9+y₁^2-4 y₁+4 & =16 x₁-8 y₁+48=0 aligned On solving Eq. (i) in Eq. (ii), we get aligned & x₁=4 & and y₁=14 aligned

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