Maths-
General
Easy

Question

The abcissa and ordinate of the end points A and B of a focal chord of the parabola y2 = 4x are respectively the roots of x2 – 3x + a = 0 and y2 + 6y + b = 0. The equation of the circle with AB as diameter is.

  1. x2 + y2 – 3x + 6y + 3 = 0    
  2. x2 + y2 – 3x + 6y – 3 = 0    
  3. x2 + y2 + 3x + 6y – 3 = 0    
  4. x2 + y2 – 3x – 6y – 3 = 0    

The correct answer is: x2 + y2 – 3x + 6y – 3 = 0


    t1 t2 = – 1 as AB is focal chord

    x2 – 3x + a = 0 ; x1 + x2 = 3 & x1x2 = a
    y2 + 6y + b = 0 ; y1 + y2 = – 6 & y1y2 = b
    x1x2 = fraction numerator 1 over denominator t subscript 1 end subscript superscript 2 end superscript end fraction. t12 = 1 = a
    y1y2 = 2t1open parentheses negative fraction numerator 2 over denominator t subscript 1 end subscript end fraction close parentheses = – 4 = b
    a = 1, b = – 4
    equation of circle AB is diameter
    x2 + y2 – 3x + 6y – 3 = 0

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