The angle between the two curves $y^2 = 4(x + 1)$ and $x^2 = 4(y + 1)$ is .............. $^\circ$.

What is the length of the chord intercepted by the parabola $y = x^2 + 3x$ on the line $x + y = 5$?

If three real normals can be drawn from a point on the $x$-axis to the parabola $y^2 = 4ax$ $(a > 0)$,what is the range of the $x$-coordinate of the point?

If the line $lx + my + n = 0$ is a tangent to the parabola $y^2 = 4ax$,then the locus of its point of contact is

If the line $x + \alpha y + \beta = 0$ touches the curve $4x^3 + 4y^3 = xy(xy + 16)$ at points $(x_1, y_1)$ and $(x_2, y_2)$,where $x_1 \neq x_2$,then the value of $\alpha + \beta$ is (given $\alpha, \beta \in R$).

The shortest distance between the line $y = x$ and the curve $y^2 = x - 2$ is