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AP EAMCET20227 Jul 2022Evening ShiftMathematicsApplication of DerivativesActual

The minimum distance of a point on the curve y=x^2-4 from the origin is

Options

  1. A15 2
  2. B19 2
  3. C15 2
  4. D19 2

Correct answer

A. 15 2

Step-by-step solution

Curve is y=x^2-4 . Minimum distance from origin is along the normal passing through origin. Consider a point on curve (h, h^2-4 ) . Slope of tangent is 2 x=2 h at (h, h^2-4 ) Slope of normal is - 1 2 h . Equation of normal is (y- (h^2-4 )=- 1 2 h (x-h) ) This passes through (0,0) . aligned & & -h^2+4 & = 1 2 & & h & = 7 2 aligned Points on the curve at minimum distance from origin can be ( 7 2 ,- 1 2 ) . Minimum distance = 7 2 + 1 4 = 15 2

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