The equation of the tangent to the parabola $y^2 = 4ax$ at the point $(a/t^2, 2a/t)$ is:

If the lines $y = x$ and $y = -x$ intersect the parabola $y^2 = 4x$ at points $A$ and $B$ respectively,other than the origin,what is the length of $AB$?

Let $P(x, y)$ be a variable point on the parabola $y = 4x^2 + 1$. Let $Q(c, c)$ be the foot of the perpendicular drawn from $P$ to the line $y = x$. If $R(h, k)$ is the mid-point of $PQ$,then the locus of $R$ is:

The length of the latus rectum of the parabola $4y^{2} + 3x + 3y + 1 = 0$ is

The condition that the two curves $y^2 = 4ax$ and $xy = c^2$ cut orthogonally is

If the normal to the parabola ${y^2} = 12x$ at the point $(3, 6)$ meets the parabola again at the point $(27, -18)$,then the equation of the circle having this normal chord as its diameter is: