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KCET2015MathematicsVector Algebra

Slope of Normal to the curve ( y=x²- 1 x² ) at ( (-1,0) ) is

Options

  1. A( 1 4 )
  2. B( 0- 1 4 )
  3. C4
  4. D(-4 )

Correct answer

A. ( 1 4 )

Step-by-step solution

Given equation of curve, [ array l y=x²- 1 x² y=x²-x⁻² array ] Differentiating both the sides, we get [ y^ =2 x-(-2) x⁻³=2 x+ 2 x³ ] [ At (-1,0), we get m₁=-2-2=-4 ] So, slope of the curve is ( -4 ) We know that, slopes of two perpendicular lines is given by [ array l m₁ m₂=-1 m₂= 1 4 array ] Hence, the slope of the normal to the curve is ( 1 4 )

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