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AP EAMCET202021 Sep 2020Evening ShiftMathematicsStraight LinesActual

The equation of the circle circumscribing the triangle formed by the straight lines (x+y=6 ). (2 x+y=4 ) and (x+2 y=5 ) is given by

Options

  1. A(x^2+y^2+17 x+19 y+50=0 )
  2. B(x^2+y^2-17 x-19 y+50=0 )
  3. C(x^2+y^2+17 x-19 y-50=0 )
  4. D(x^2+y^2-17 x+19 y-50=0 )

Correct answer

B. (x^2+y^2-17 x-19 y+50=0 )

Step-by-step solution

Equation of circle circumscribing the triangle formed by the straight lines, (x+y=6,2 x+y=4 ) and (x+2 y=5 ) is ( aligned & (x+y-6)(2 x+y-4)+ (2 x+y-4)(x+2 y-5) & + (x+2 y-5)(x+y-6)=0 aligned ) ( ) For a circle the coefficients of terms (x^2 ) and (y^2 ) must be equal and non-zero and coefficient of (x y ) must be zero. ( ) Coefficient of (x^2= ) coefficient of (y^2 ) ( 2+2 + =1+2 +2 =1 ) and coefficient of (x y=0 ) ( 1+2+4 + + +2 =0 =-6 / 5 . ) So, equation of required circle is ( array ll (x+y-6)(2 x+y-4)- 6 5 (2

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