The tangent at the point $(1, 2)$ to the curve $y^2 = 4x$ makes an angle $\theta$ with the positive direction of the $X$-axis. Then $\theta =$ (in $^{\circ}$)

What is the equation of the tangent to the curve $x^2 = -4y$ at the point $(-4, -4)$?

Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$,passing through $(2, 3)$,and the axis is along the $x$-axis.

Let $P(at^{2}, 2at)$, $Q$, and $R(ar^{2}, 2ar)$ be three points on the parabola $y^{2}=4ax$. If $PQ$ is a focal chord and $PK$ is parallel to $QR$, where the coordinates of $K$ are $(2a, 0)$, then the value of $r$ is:

If the normal to the parabola $y^2=4x$ at $P(1,2)$ meets the parabola again at $Q$,then the coordinates of $Q$ are

The equation of the tangent at $P(-4, -4)$ on the curve $x^{2} = -4y$ is