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MHT CET202019 Oct 2020Morning ShiftMathematicsDifferential EquationsActual

The differential equation of the circles having their centres on the line y =8 and touching the X -axis is

Options

  1. A(y-8)² [1- ( d y d x )² ]=64
  2. B(y-8)² [1+ ( d y d x )² ]=64
  3. C(y-8) [1+ ( d y d x )² ]=64
  4. Dy² (1+ d y d x )=64

Correct answer

B. (y-8)² [1+ ( d y d x )² ]=64

Step-by-step solution

(B) Let ( h , 8) be the centre of the circle. Since circle touches X axis, radius =8 (x-h)²+(y-8)²=(8)² ...(1) Differentiating w.r.t. x, we get aligned & 2(x-h)+2(y-8) d y d x =0 &(x-h)=-(y-8) d y d x aligned Substituting value of (x-h) in eq. (1), we get aligned & [-(y-8) d y d x ]²+(y-8)²=64 &(y-8)² [ ( d y d x )²+1 ]=64 aligned

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