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What is the differential equation of all parabolas of the type y^2=4 a(x-b) ?

Options

  1. Ad^2 y d x^2 + ( d y d x )^2=0
  2. Bd^2 y d x^2 +x^2 ( d y d x )^2=0
  3. Cy^2 d^2 y d x^2 + ( d y d x )^2=0
  4. Dy d^2 y d x^2 + ( d y d x )^2=0

Correct answer

D. y d^2 y d x^2 + ( d y d x )^2=0

Step-by-step solution

Since, y^2=4 a x-4 a b 2 y d y d x =4 a y d^2 y d x^2 + ( d y d x )^2=0

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