The normal to the curve $x^{2}=4y$ passing through $(1,2)$ is

Let $P$ be a point on the parabola $y^{2}=12x$ and $N$ be the foot of the perpendicular drawn from $P$ on the axis of the parabola. $A$ line is drawn through the mid-point $M$ of $PN$,parallel to the axis of the parabola,which meets the parabola at $Q$. If the $y$-intercept of the line $NQ$ is $\frac{4}{9}$,then:

An equilateral triangle is inscribed in the parabola $y^2=16ax$ with one of its vertices at the origin. Then,the centroid of that triangle is

Let $\alpha_1$ and $\alpha_2$ be the ordinates of two points $A$ and $B$ on a parabola $y^2=4ax$ and let $\alpha_3$ be the ordinate of the point of intersection of its tangents at $A$ and $B$. Then,$\alpha_3-\alpha_2=$

For the curve $y^2 = 4ax$,the lengths of the tangent,subtangent,normal,and subnormal at the point $(at^2, 2at)$ are respectively:

The equation of a tangent line to the parabola $y^2 = 8x$,which passes through the point $(1, 3)$,is: