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JEE Advanced2006MathematicsParabolaActual

Match the column. Normals at P, Q, R are drawn to y^2=4 x which intersect at (3,0) . Then,

Options

  1. A(i) (a), (ii) (b), (iii) (d), (iv) (c)
  2. B(i) (b), (ii) (a), (iii) (d), (iv) (c)
  3. C(i) (a), (ii) (b), (iii) (c), (iv) (d)
  4. D(i) (b), (ii) (a), (iii) (c), (iv) (d)

Correct answer

A. (i) (a), (ii) (b), (iii) (d), (iv) (c)

Step-by-step solution

Since, equation of normal is y+x t=2 a t+a t^3 passes through (3,0) . 3 t=2 t+t^3 t=0,1,-1 . P(1,2), Q(0,0), R(1,-2) . Thus, (i) Area of P Q R= 1 2 1 4=2 (ii) Centroid of P Q R= ( 2 3 , 0 ) Equation of circle passing through P, Q, R is aligned & (x-1)(x-1)+(y-2)(y+2)+ (x-1)=0 & 1-4- =0 =-3 & Required equation of circle is x^2+y^2-5 x-1=0 & Centre ( 5 2 , 0 ) and radius 5 2 . aligned

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