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The value of λ for which the curve 7 x + 5 2 + 7 y + 3 2 = λ 2 4 x + 3 y - 24 2 represents a parabola, is

Options

  1. A± 6 5
  2. B± 7 5
  3. C± 1 5
  4. D± 2 5

Correct answer

B. ± 7 5

Step-by-step solution

Given, curve is 7 x + 5 2 + 7 y + 3 2 = λ 2 4 x + 3 y - 24 2 , ⇒ 7 x + 5 7 2 + 7 y + 3 7 2 = λ 2 4 2 + 3 2 2 × 4 x + 3 y - 24 4 2 + 3 2 2 , ⇒ 49   x + 5 7 2 + y + 3 7 2 = 25 λ 2 4 x + 3 y - 24 4 2 + 3 2 2 , ⇒ x + 5 7 2 + y + 3 7 2 = 25 λ 2 49 4 x + 3 y - 24 4 2 + 3 2 2 , ⇒ x + 5 7 2 + y + 3 7 2 = 5 λ 7 × 4 x + 3 y - 24 4 2 + 3 2 . The L . H . S . of the above equation represent distance of a point x , y from a point - 5 7 , - 3 7 and R . H . S . repres

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