The equation of the directrix for the parabola $4x^{2}-4x-2y+3=0$ is

Consider the circle $C: x^2+y^2=4$ and the parabola $P: y^2=8x$. If the set of all values of $\alpha$,for which three chords of the circle $C$ on three distinct lines passing through the point $(\alpha, 0)$ are bisected by the parabola $P$,is the interval $(p, q)$,then $(2q-p)^2$ is equal to.............

Consider the parabola with vertex $\left(\frac{1}{2}, \frac{3}{4}\right)$ and the directrix $y=\frac{1}{2}$. Let $P$ be the point where the parabola meets the line $x=-\frac{1}{2}$. If the normal to the parabola at $P$ intersects the parabola again at the point $Q$,then $(PQ)^{2}$ is equal to :

If the line $2x + 3y + n = 0$ is a tangent to the parabola $y^2 = 8x$,then the equation of the normal drawn at the point $(2n, 4\sqrt{n})$ to the parabola $y^2 = 8x$ is

The number of normals drawn to the parabola $y^2=4x$ from the point $(1,0)$ is

The vertices of the base of an isosceles triangle lie on a parabola $y^2=4x$ and the base is a part of the line $y=2x-4$. If the third vertex of the triangle lies on the $X$-axis,its coordinates are