The equations of the tangents to the parabola $y^2 = 4ax$ at the ends of its latus rectum are-

If one end of a focal chord of the parabola $y^2 = 16x$ is $(1, -4)$,find the other end.

The point on the curve $y^2=2(x-3)$ at which the normal is parallel to the line $y-2x+1=0$ is

Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$,passing through $(2, 3)$,and the axis is along the $x$-axis.

If a normal chord of a parabola $y^2 = 4ax$ subtends a right angle at the origin,then the slope of that normal chord is

$(1, 1)$ is the vertex and $x+y+1=0$ is the directrix of a parabola. If $(a, b)$ is its focus and $(c, d)$ is the point of intersection of the directrix and the axis of the parabola,then $a+b+c+d=$