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BITSAT2015MathematicsApplication of DerivativesActual

The line which is parallel to X-axis and crosses the curve y= x at an angle of 45^ , is

Options

  1. Ax= 1 4
  2. By= 1 4
  3. Cy= 1 2
  4. Dy=1

Correct answer

C. y= 1 2

Step-by-step solution

Given equation of a line parallel to X-axis is y = k Given equation of the curve is y= x , On solving equation of line with the equation of curve, we get x=k² Thus the intersecting point is ( k ², k ) It is given that the line y = k intersect the curve y= x at an angle of / 4 . This means that the slope of the tangent to y = x at ( k ², k ) is ( 4 )= 1 array l ( dy dx )_ ( k ², k ) = 1 ( 1 2 x )_ ( k ², k ) = 1 k = 1 2 array

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