WBJEE · Maths · Application of Derivatives
The normal to the curve \(y=x^{2}-x+1\), drawn at the points with the abscissa \(x_{1}=0, x_{2}=-1\) and \(x_{3}=5 / 2\)
- A are paraliel to each other
- B are pairwise perpendicular
- C are concurrent
- D are not concurrent
Answer & Solution
Correct Answer
(C) are concurrent
Step-by-step Solution
Detailed explanation
Given equation of curve. \[ \begin{aligned} y &=x^{2}-x+1 \\ \Rightarrow \quad & \frac{d y}{d x}=2 x-1 \end{aligned} \] Slope of normal \(=\frac{1}{1-2 x}\) Now, at \(x_{1}=0, y_{1}=1\) \(\therefore\) Slope of normal at \((0,1)=1\) \(\therefore\) Equation of normal,…
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