The tangent at the point $(2, -2)$ to the curve $x^2y^2 - 2x = 4(1 - y)$ does not pass through the point:

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

The length of the subtangent at any point of the curve $x^my^n = a^{m+n}$ is proportional to

If the curves $y^2 = 12x - 3$ and $y^2 = 12 - kx$ cut each other orthogonally, then the length of the sub-tangent at $(1, b)$ on the curve $y^2 = 12 - kx$ is

If the tangent drawn at a point $P$ on the curve $y=3x^2-5x+7$ is parallel to its chord joining the points $(1, y_1)$ and $(2, y_2)$ on it, then the $x$-coordinate of the point $P$ is

If the tangent to the curve $y^{2} = x^{3}$ at $(m^{2}, m^{3})$ is also a normal to the curve at $(M^{2}, M^{3})$, then the value of $mM$ is