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Most Important Selected Qs for JEE AdvancedMathematicsParabola

If PQ is a chord of parabola x^2=4 y which subtends right angle at vertex. Then locus of centroid of triangle PSQ ( S is focus) is a parabola whose -

Options

  1. Avertex is (0,3)
  2. Blength of L R is 4 / 3
  3. Caxis is x =0
  4. Dtangent at the vertex is x=3

Correct answer

C. axis is x =0

Step-by-step solution

aligned & Let P (2 t ₁ t ₁^2 ), Q (2 t ₂ t ₂^2 ) & m _ OP m _ OQ =-1 t ₁ 2 t ₂ 2 =-1 & t ₁ t ₂=-4 aligned Let centroid G(h, k) aligned & so h = 2 t ₁+2 t ₂ 3 , k = t ₁^2+ t ₂^2+1 3 & 3 k -1= ( t ₁+ t ₂ )^2-2 t ₁ t ₂ & 3 k -1= ( 3 ~h 2 )^2+8 & 3( k -3) 4=9 ~h ^2 3 x ^2=4( y -3) aligned so vertex (0,3), LR = 4 3 , axis x =0 , tangent at vertex y =3

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