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AP EAMCET20228 Jul 2022Morning ShiftMathematicsDifferential EquationsActual

The equation of the family of curves for which length of the sub normal at any point ( x , y ) is always a constant ( k ) is

Options

  1. Ay^2=4 a x
  2. By ^2- A =2 Kx
  3. Cy^2-K=2 x
  4. Dy^2=K(x+K)

Correct answer

B. y ^2- A =2 Kx

Step-by-step solution

Length of subnormal is ( y , m )= k aligned & y dy dx = k & ydy = kdx & y ^2 2 = kx & y ^2= 2 kx + A & y ^2- A = 2 kx aligned

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