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AP EAMCET202422 May 2024Evening ShiftMathematicsDifferential EquationsActual

The differential equation of the family of hyperbola having their centres at origin and their axes along the coordinates axes is

Options

  1. Ax y y₂+x y₁^2-y y₁=0
  2. Bx y₂-x y y₁^2+y y₁=0
  3. Cx y y₂+x y₁^2+y y₁=0
  4. Dx y₂+x y₁^2-y y₁=0

Correct answer

A. x y y₂+x y₁^2-y y₁=0

Step-by-step solution

Let equation of hyperbola be x^2 a^2 + y^2 b^2 =1 2 x a^2 + 2 y b^2 d y d x =0 y x ( d y d x )= -b^2 a^2 Differentiate w.r.t. x, y x ( d^2 y d x^2 )+ x ( d y d x )^2-y d y d x x^2 =0 x y y₂+x (y₁ )^2-y y₁=0

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