If the directrix of the parabola $x^2+4y-6x+\lambda=0$ is $y+1=0$,then which of the following is correct?

Let $(x, y)$ be any point on the parabola $y^2 = 4x$. Let $P$ be a point that divides the line segment from $(0, 0)$ to $(x, y)$ in the ratio $1 : 3$. Find the locus of $P$.

If $mx - y + c = 0$ is a normal at a point $P$ on the parabola $y^2 = 16x$ and the focal distance of $P$ is $40$ units,then $|c| =$

The point on the curve $4y^2 - 4y + 2x - 1 = 0$ at which the tangent becomes parallel to the $Y$-axis is:

Find the area of the triangle formed by the lines joining the vertex of the parabola $x^{2}=12y$ to the ends of its latus rectum. (in $\text{ unit}^{2}$)

The focal distance of a point on the parabola $y^{2}=16x$ whose ordinate is twice the abscissa,is