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The curve passing through P 2 , 7 2 and having slope 1 - 1 x 2 at P x , y also passes through

Options

  1. A- 2 , 2 3
  2. B- 2 , - 3 2
  3. C- 2 , 1
  4. D- 2 , 6

Correct answer

B. - 2 , - 3 2

Step-by-step solution

As d y d x = 1 - 1 x 2 ⇒ d y = 1 - 1 x 2 d x Integrating, we get ∫ dy = ∫ 1 - 1 x 2 d x ⇒ y = x + 1 x + C As it passes through 2 , 7 2 ∴ 7 2 = 2 + 1 2 + C ⇒ C = 1 Thus, y = x + 1 x + 1 which also passes through - 2 , - 3 2

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