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AP EAMCET201920 Apr 2019Morning ShiftMathematicsCircleActual

The abscissae of two points (P, Q ) are the roots of the equation (2 x^2+4 x-7=0 ) and their ordinates are the roots of the equation (3 x^2-12 x-1=0 ). Then the centre of the circle with (P Q ) as a diameter is

Options

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

Correct answer

A. ((-1,2) )

Step-by-step solution

Since, it is given that abscissae of two point (P, Q ) are roots of the equation (2 x^2+4 x-7=0 ) and their ordinates are the roots of the equation (3 x^2-12 x-1=0 ). Let (P (x₁, y₁ ) ) and (Q (x₂, y₂ ) ), then (x₁+x₂=-2 and y₁+y₂=4 ) Now, centre of the circle with (P Q ) as a diameter is ( ( x₁+x₂ 2 , y₁+y₂ 2 )=(-1,2) . ) Hence, option (1) is correct.

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