The length of the subtangent to the curve $x^2 y^2 = a^4$ at the point $(-a, a)$ is

Find the equation of the tangent to the curve $y + \frac{2}{x - 3} = 0$ which has a slope of $2$.

$f(x)$ is a continuous function on $\mathbb{R}$ and $y=f(x)$ is a curve. If $(\alpha, \beta)$ is a point such that $\beta=f(\alpha)$ and $p\alpha+m\beta+n=0$ $(p \neq 0, m \neq 0)$,then which one of the following is true?

Show that the tangents to the curve $y=7x^3+11$ at the points where $x=2$ and $x=-2$ are parallel.

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 angle of intersection of the curves $y = x^2$ and $x = y^2$ at $(1, 1)$ is