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COMEDK2020MathematicsApplication of Derivatives

The point on the curve y²=x , the tangent at which makes an angle 45^ with X -axis is

Options

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

Correct answer

B. (1 / 4,1 / 2)

Step-by-step solution

We have, gathered y²=x 2 y d y d x =1 d y d x = 1 2 y gathered Let the required point be (x₁, y₁ ) , So, slope of tangent aligned &= . d y d x |_ (x₁-w₁ ) & m= 1 2 y₁ aligned Since, tangent makes 45⁵ with X -axis, so m= 45^ =1 From Eqs, (i) and (ii), we have 1 2 q₁ =1 f₁= 1 2 Again, (x₁, y₁ ) lies on th curve y^ Z =x₁ So, y₁²=x₁ x₁= ( 1 2 )²= 1 4 So, required point is ( 1 4 , 1 2 ) .

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