Maths-
General
Easy

Question

The tangent at P to a parabola y2 = 4ax meets the directrix at U and the latus rectum at V then SUV (where S is the focus) :

  1. must be a right triangle    
  2. must be an equilateral triangle    
  3. must be an isosceles triangle    
  4. must be a right isosceles triangle    

The correct answer is: must be an isosceles triangle


    V equals open parentheses a comma fraction numerator a open parentheses 1 plus t to the power of 2 end exponent close parentheses over denominator t end fraction close parentheses text  and  end text T colon t y equals x plus a t to the power of 2 end exponent text  put  end text x equals a & x equals negative a


    Alternatively: PU subtends a right angles at focus Þ isosceles

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