The length of the latus rectum of the parabola ${y^2} = 5x + 4y + 1$ is

Variable straight lines $y=mx+c$ make intercepts on the curve $y^2-4ax=0$ which subtend a right angle at the origin. Then the point of concurrence of these lines $y=mx+c$ is

Find the equation of the normal to the parabola $y^2 = 4x$ passing through the point $(3, 0)$.

Find the locus of the midpoint of the chord of the parabola $y^2 = 4x$ drawn from the vertex.

The normal meets the parabola $y^2 = 4ax$ at a point where the abscissa is equal to the ordinate. Find this point.

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