The equation of the normal to the curve $y = \sin x$ at the point $(0, 0)$ is

The tangent to the curve $y = x^{3} + 1$ at $(1, 2)$ makes an angle $\theta$ with the $y$-axis. Then the value of $\tan \theta$ is

The coordinates of the point on the curve $y=x^2-3x+2$ where the tangent is perpendicular to the straight line $y=x$ are

The lengths of tangent, subtangent, normal and subnormal for the curve $y=x^2+x-1$ at $(1,1)$ are $A, B, C$ and $D$ respectively, then their increasing order is

Let $y=f(x)$ be any curve on the $X-Y$ plane and $P$ be a point on the curve. Let $C$ be a fixed point not on the curve. If the length $PC$ is either a maximum or a minimum, then:

If the line $ax + by + c = 0$ is a normal to the curve $xy = 1$,then