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COMEDK2017MathematicsParabola

Find the point on the curve y=x² , where the slope of the tangent is equal to the x coordinate of the point.

Options

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

Correct answer

D. (0,0)

Step-by-step solution

Let the required point be P (x₁, y₁ ) The given curve is y=x²...(i) Differentiating Eq. (i) w.r.t. x , we get d y d x =2 x Slope of tangent at P (x₁, y₁ )=2 x But the slope of tangent at aligned & P (x₁, y₁ )=x -coordinate of P & 2 x₁=x₁ 2 x₁-x₁=0 & x₁=0 aligned As P (x₁, y₁ ) lies on the curve, we get y₁=x₁² y₁=0 Hence, the required point is (0, J) .

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