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Manipal MET2013MathematicsParabola

Minimum distance between the curves y^2=4 x and x^2+y^2-12 x+31=0 is

Options

  1. A5
  2. B21
  3. C28 - 5
  4. D21 - 5

Correct answer

A. 5

Step-by-step solution

Centre and radius of the given circle is P(6,0) and 5 , respectively. Now minimum distance between two curves always occurs along a line which normal to both the curves. Equation of normal to y^2=4 x at (t^2, 2 t ) is y=-t x+2 t+t^3 If it is normal to circle also, then it must pass though (6,0) . 0=t^3-4 t t=0 or t= 2 . aligned & A(4,4) and C(4,-4) & P A=P C= 20 =2 5 . & Required minimum distance =2 5 - 5 = 5 aligned

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