What is the equation of the tangent to the parabola $y^2 = 4x$ at the point $(1, 2)$?

The axis of a parabola is parallel to the $Y$-axis. If this parabola passes through the points $(1,0), (0,2), (-1,-1)$ and its equation is $ax^2 + bx + cy + d = 0$,then $\frac{ad}{bc} = $

The perpendicular distance from the origin to the focal chord drawn through the point $(4, 5)$ to the parabola $y^2 - 4y - 3x + 7 = 0$ is

At what point on the parabola $y^2 = 4x$ does the normal make equal angles with the coordinate axes?

The vertex of the parabola $x^2 + 8x + 12y + 4 = 0$ is

Let $y^2=12x$ be a parabola and $S$ be its focus. Let $PQ$ be a focal chord of the parabola such that $(SP)(SQ)=\frac{147}{4}$. Let $C$ be the circle described taking $PQ$ as a diameter. If the equation of circle $C$ is $64x^2+64y^2-\alpha x-64\sqrt{3}y=\beta$,then $\beta-\alpha$ is equal to . . . . . .