COMEDK · Maths · 13. Parabola
Find the point on the curve \(y=x^{2}\), where the slope of the tangent is equal to the \(x\) coordinate of the point.
- A \((1,1)\)
- B \((-1,-1)\)
- C \((1,2)\)
- D \((0,0)\)
Answer & Solution
Correct Answer
(D) \((0,0)\)
Step-by-step Solution
Detailed explanation
Let the required point be \(\boldsymbol{P}\left(x_{1}, y_{1}\right)\) The given curve is \(y=x^{2}...(i)\) Differentiating Eq. (i) w.r.t. \(x\), we get \(\frac{d y}{d x}=2 x \Rightarrow\) Slope of tangent at \(P\left(x_{1}, y_{1}\right)=2 x\) But the slope of tangent at…
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