If $lx + my + n = 0$ is tangent to the parabola $x^2 = y$,then the condition of tangency is

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

Let $P$ be the parabola in the plane determined by the equation $y = x^2$. Suppose a circle $C$ in the plane intersects $P$ at four distinct points. If three of these points are $(17, 289), (-2, 4), (13, 169)$,then the sum of the perpendicular distances from the directrix of $P$ to all four of the intersection points is:

The point of intersection of the normals to the parabola $y^2 = 4x$ at the ends of its latus rectum is

What is the value of the parameter $t$ for the point $(2, 6)$ on the parabola $y^2 = 18x$?

Consider the conic $C: 25(x - 1)^2 + 25(y + 1)^2 = (3x - 4y)^2$. If the curve $E$ is the locus of the point of intersection of perpendicular tangents to the conic $C$,then the minimum distance between the curve $E$ and the point $(2, -1)$ is: