Maths-
General
Easy

Question

If normal at point P on parabola y2 = 4ax, (a > 0) meet it again at Q is such a way that OQ is of minimum length where O is vertex of parabola, then ΔOPQ is

  1. a right angled triangle    
  2. obtuse angled triangle    
  3. acute angled triangle    
  4. None    

The correct answer is: a right angled triangle


    thereforeNormal at P(t1) meets at Q(t2)
    t2 = negative fraction numerator 2 over denominator t subscript 1 end subscript end fraction minus t subscript 1 end subscript

    open vertical bar t subscript 2 end subscript close vertical bar greater or equal than 2 square root of 2
    For minimum length of OQ, |t2| should be minimum
    therefore i.e. | t2 | = 2 square root of 2
    If t2 = negative 2 square root of 2 rightwards double arrow t1 = square root of 2
    Slope of OQ = fraction numerator 2 over denominator t subscript 2 end subscript end fraction = m1 and of OQ = fraction numerator 2 over denominator t subscript 1 end subscript end fraction = m2
    therefore m1m2 = –1 therefore capital deltaOPQ is right angled triangle.

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