What is the focus of the parabola $y^2 - x - 2y + 2 = 0$?

Let $S$ be the focus of the parabola $y^2=4ax$ and $PQ$ be a focal chord such that $SP=\alpha$ and $SQ=\alpha^{\prime}$. Then $\frac{1}{\alpha}+\frac{1}{\alpha^{\prime}}=$

The chord $PQ$ of the parabola $y^2 = x$,where one end $P$ of the chord is at point $(4, -2)$,is perpendicular to the axis of the parabola. Then the slope of the normal at $Q$ is

The maximum area of a circle centered at the origin,which is inscribed in the parabola $y = x^2 - 100$,can be expressed as $\frac{a\pi}{b}$,where $a$ and $b$ are coprime numbers. Then the value of $a + b$ is:

If a normal chord at a point $t$ on the parabola $y^2=4ax$ subtends a right angle at the vertex,then $t^2$ equals to

The normal at a point on the parabola $y^2 = 4x$ passes through a point $P$. Two more normals to this parabola also pass through $P$. If the centroid of the triangle formed by the feet of these three normals is $G(2,0)$,then the abscissa of $P$ is