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Manipal MET2016MathematicsParabola

The coordinates of the point on the parabola y=x^2+7 x+2 , which is nearest to the straight line y=3 x-3 , are

Options

  1. A(-2,-8)
  2. B(1,10)
  3. C(2,20)
  4. D(-1,-4)

Correct answer

A. (-2,-8)

Step-by-step solution

Any point on the parabola is (x, x^2+7 x+2 ) Its distance from the line y=3 x-3 is given by aligned p & = | 3 x- (x^2+7 x+2 )-3 9+1 | & = | x^2+4 x+5 10 | aligned = x^2+4 x+5 10 [ . as .x^2+4 x+5 0, x R ] aligned & & d p d x & =0 & & x & =-2 aligned So, the required point is (-2,-8) .

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