If $(h, k)$ is the point to which the origin is shifted in order to transform the equation $y^2-4x+6y+17=0$ into the form $Y^2=4aX$,then $h^2+k^2=$

Let $Z$ be the point of intersection of the axis and the directrix of the parabola $4x^2 - 12x + 4y + 5 = 0$. If $S$ is its focus,then the point which divides $SZ$ in the ratio $2:1$ is

Tangents are drawn from the point $(-1, 2)$ to the parabola $y^2 = 4x$. The length of the intercept made by these tangents on the line $x = 2$ is:

Assertion $(A)$: The curves $y^2 = 4x$ and $x^2 = -2y$ intersect at $(0,0)$ and $(2, -2)$ orthogonally.
Reason $(R)$: If the product of the slopes of the tangents drawn to two curves at their point of intersection is $-1$,then the curves are said to cut each other orthogonally. The correct option among the following is:

The line $y=x+1$ is a tangent to the curve $y^{2}=4x$ at the point

If $x-2y+k=0$ is a tangent to the parabola $y^2-4x-4y+8=0$,then the slope of the tangent drawn at $(1, k)$ on the given parabola is