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Manipal MET2010MathematicsParabola

If the normal to the parabola y^2=4 a x at the point (a t^2, 2 a t ) cuts the parabola again at (a T^2, 2 a T ) , then

Options

  1. A-2 T 2
  2. BT (- ,-8) (8, )
  3. CT^2 8
  4. DT^2 8

Correct answer

D. T^2 8

Step-by-step solution

Equation of the normal of the parabola y^2=4 a x at the point (a t^2, 2 a t ) is y+t x=2 a t+a t^3...(i) Eq. (i) cuts the parabola again at (a T^2, 2 a T ) . Then, 2 a T+t a T^2=2 a t+a t^3 2 a(T-t)=-a t (T^2-t^2 ) 2=-t(T+t) ( t T) t^2+t T+2=0 t is real, T^2-4 1 2 0 T^2 8

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