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Paragraph: Let S: 4 x^2-4 x-24 y+49=0 is a parabola and S₁=0 represent locus of middle point of chords of parabola S=0 , which passes through origin. L₁ & L₂ are the tangents for S=0 and normals for x^2+y^2=72 On the basis of above informations, answer the following questions: Question: Sum of the slopes of L₁ and L₂ is -

Options

  1. A7 3
  2. B- 7 3
  3. C- 1 3
  4. D- 4 3

Correct answer

C. - 1 3

Step-by-step solution

aligned & 4 x^2-4 x+1=24 y-48 & (2 x-1)^2=24(y-2) & (x- 1 2 )^2=6(y-2) aligned aligned & L₁ L₂ must be in the form of y=m x & solving it with S=0 & 4 x^2-4 x-24 m x+49=0 & 4 x^2-4 x(1+6 m)+49=0 & by D=0 16(6 m+1)^2-16.49=0 & 6 ~m +1= 7 ~m =1 or - 4 3 & m₁+m₂=- 1 3 aligned

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