Question

The normals to the curve \(y=x^{2}-x+1\), drawn at the points with the abscissa \(x_{1}=0, x_{2}=-1\) and \(x_{3}=\frac{5}{2}\)
(A) are parallel to each other
(B) are pair wise perpendicular
(C) are concurrent
(D) are not concurrent

Answer 1

Ans: (C)
Hint : The three normals are
$$
\begin{aligned}
&x-y+1=0 \\
&x-3 y+10=0 \\
&2 x+8 y-43=0
\end{aligned}
$$