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KCET2017MathematicsVector Algebra

The point on the curve ( y²=x ) where the tangent makes an angle of ( / 4 ) with ( x )-axis is

Options

  1. A( ( 1 2 , 1 4 ) )
  2. B( ( 1 4 , 1 2 ) )
  3. C( (4,2) )
  4. D( (1,1) )

Correct answer

B. ( ( 1 4 , 1 2 ) )

Step-by-step solution

Given that, ( y²=x (1) ) Slope of the curve is given by ( m= d y d x ) And we know that, ( m= ) Here, ( = I I 4 ) so, ( m= ( I 4 )=1 ) Now, differentiating Eq. (1) with respect to ( x ), we get ( 2 y d y d x =1 ) ( 2 y 1=1 ) ( y= 1 2 ) So, ( x= 1 4 ) Therefore, point is ( ( 1 4 , 1 2 ) )

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