If ${x^2} + 6x + 20y - 51 = 0$,then the axis of the parabola is

The locus of the point of intersection of the perpendicular tangents to the curve $y^2 + 4y - 6x - 2 = 0$ is:

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

Let $A$ and $B$ be two distinct points on the parabola $y^{2}=4x$. If the axis of the parabola touches a circle of radius $r$ having $AB$ as its diameter, then the slope of the line $AB$ is

The equation of the tangent to the parabola $y^2=16x$,which is perpendicular to the line $3x-4y+5=0$,is given by

If the focal chord drawn through the point $(1,2)$ to the parabola $y^2=8x$ meets this parabola in $(x_1, y_1)$ and $(x_2, y_2)$,then $x_1+x_2=$