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AP EAMCET2004MathematicsParabola

Match the points on the curve 2 y^2=x+1 with the slopes of normals at those points and choose the correct answer.

Options

  1. Aarray llll A & B & C & D 2 & 4 & 3 & 1 array
  2. Barray llll A & B & C & D 2 & 5 & 3 & 1 array
  3. Carray llll A & B & C & D 2 & 3 & 5 & 1 array
  4. Darray llll A & B & C & D 2 & 5 & 1 & 3 array

Correct answer

B. array llll A & B & C & D 2 & 5 & 3 & 1 array

Step-by-step solution

Given equation of curve is 2 y^2=x+1 On differentiating both sides w.r.t. x , we get 4y d y d x =1 d y d x = 1 4 y The slope of the normal is d x d y =-4 y I. d x d y_ (7,2) =-4(2)=-8 II. d x d y_ (0, 1 2 ) = -4 2 =-2 2 III. d x d y_ (1,-1) =-4(-1)=4 IV. d x d y_ (3, 2 ) =-4( 2 )=-4 2 Option (2) satisfy the all four statements.

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