The equation $y^{2}+4x+4y+k=0$ represents a parabola whose latus rectum is

The straight line $y = 2x + \lambda$ does not meet the parabola $y^2 = 2x$,if

If $x + y = k$ is a normal to the parabola $y^2 = 12x$,then what is the value of $k$?

The number of points on the parabola $y^2=x$ at which the slope of the normal drawn at the point is equal to the $x$-coordinate of that point is

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

At which point does the line $x = my + \frac{a}{m}$ touch the parabola $x^2 = 4ay$?