The normals to the curve $y=x^{2}-x+1$,drawn at the points with the abscissae $x_{1}=0, x_{2}=-1$ and $x_{3}=5/2$,are:

If the tangent to the curve $x^{2/3} + y^{2/3} = a^{2/3}$ meets the $X$-axis at $A$ and $Y$-axis at $B$,then $AB =$

Co-ordinates of a point on the curve $y = x \log x$ at which the normal is parallel to the line $2x - 2y = 3$ are

The point at which the tangent line to the curve of $y=\frac{16}{x}-x^2$ is horizontal,is

If the straight line $x \cos \alpha + y \sin \alpha = p$ touches the curve $(\frac{x}{a})^n + (\frac{y}{b})^n = 2$ at the point $(a, b)$ on it and $\frac{1}{a^2} + \frac{1}{b^2} = \frac{k}{p^2}$,then $k =$

If the tangent to the curve $y = \frac{x}{x^2-3}$,$x \in R, (x \neq \pm \sqrt{3})$ at a point $(\alpha, \beta) \neq (0,0)$ on it,is parallel to the line $2x + 6y - 11 = 0$,then