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KVPY2011MathematicsStraight Lines

Let A=(4,0), B=(0,12) be two points in the plane. The locus of a point C such that the area of triangle A B C is 18 sq. units is -

Options

  1. A(y+3 x+12)²=81
  2. B(y+3 x+81)²=12
  3. C(y+3 x-12)²=81
  4. D(y+3 x-81)²=12

Correct answer

C. (y+3 x-12)²=81

Step-by-step solution

1 2 | array ccc 1 & x & y 1 & 0 & 12 1 & 4 & 0 array |= 181(-48)-x(-12)+y(4)= 3612 x+4 y-48= 363 x+y-12= 9(3 x+y-12)²=81

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