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Question

Let y2 = 4ax be parabola and PQ be a focal chord of parabola. Let T be the point of intersection of tangents at P and Q. Then

  1. area of circumcircle of ΔPQT is open parentheses fraction numerator pi left parenthesis P Q right parenthesis to the power of 2 end exponent over denominator 4 end fraction close parentheses    
  2. orthocenter of ΔPQT will lie on tangent at vertex.    
  3. incenter of ΔPQT will be vertex of parabola.    
  4. incentre of ΔPQT will lie on directrix of parabola.    

The correct answer is: area of circumcircle of ΔPQT is open parentheses fraction numerator pi left parenthesis P Q right parenthesis to the power of 2 end exponent over denominator 4 end fraction close parentheses



    for focal chord t1t2 = – 1
    Tangent drawn at the extremities of focal chord are perpendicular and meet at directrix
    straight angle PTQ = 90º
    Hence PQ is diameter of circum circle of ΔPTQ.
    2r = PQ rightwards double arrowr = (PQ/2)
    Area of circum circle pi r squared = fraction numerator pi left parenthesis P Q right parenthesis to the power of 2 end exponent over denominator 4 end fraction

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