AP EAMCET202419 May 2024Evening ShiftMathematicsParabolaActual

The normal drawn at a point (2,-4) on the parabola y^2=8 x cuts again the same parabola at ( , ) then + =

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Correct answer

D. 30

Step-by-step solution

Given the parabola, y^2=8 x a=2 Now, given a point on y^2=8 x is (2,-4) (2,-4)= (a t^2, 2 a t ) (2,-4)= (2 t^2, 4 t ) t=-1 Since, normal drawn at (2,-4) again meet at ( , ) So, ( , )= (2 t₂^2, 2 a t₂ ) where t₂=-t- 2 t =+1+2=3 ( , )= (2 3^2, 2 2 3 )=(18,12) So, + =30 .

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