From the point $(-1, -60)$ two tangents are drawn to the parabola $y^2 = 4x$. Then the angle between the two tangents is .................. $^o$

If a circle with its centre at the focus of the parabola $y^2 = 2px$ is such that it touches the directrix of the parabola,then a point of intersection of the circle and the parabola is

If the line segment joining the vertex of the parabola $y^2=4ax$ and a point on the parabola makes an angle $\theta$ with the positive $X$-axis,then the length of that line segment is

Let $a, r, s, t$ be nonzero real numbers. Let $P(at^2, 2at)$,$Q(at'^2, 2at')$,$R(ar^2, 2ar)$,and $S(as^2, 2as)$ be distinct points on the parabola $y^2=4ax$. Suppose that $PQ$ is the focal chord and lines $QR$ and $PK$ are parallel,where $K$ is the point $(2a, 0)$.
$1.$ The value of $r$ is
$(A) -\frac{1}{t}$ $(B) \frac{t^2+1}{t}$ $(C) \frac{1}{t}$ $(D) \frac{t^2-1}{t}$
$2.$ If $st=1$,then the tangent at $P$ and the normal at $S$ to the parabola meet at a point whose ordinate is
$(A) \frac{(t^2+1)^2}{2t^3}$ $(B) \frac{a(t^2+1)^2}{2t^3}$ $(C) \frac{a(t^2+1)^2}{t^3}$ $(D) \frac{a(t^2+2)^2}{t^3}$
Give the answer for question $1$ and $2$.

$PQ$ is a double ordinate of the parabola $y^2 = 4ax$. The locus of the points of trisection of $PQ$ is

For the parabola represented in the parametric form by $x=t^2+t+1$ and $y=t^2-t+1$,the length of the latus rectum is