The point of intersection of the latus rectum and axis of the parabola $y^2+4x+2y-8=0$ is

Let $O$ be the vertex of the parabola $x^{2}=4y$ and $Q$ be any point on it. Let the locus of the point $P$, which divides the line segment $OQ$ internally in the ratio $2:3$, be the conic $C$. Then the equation of the chord of $C$, which is bisected at the point $(1, 2)$, 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,$\alpha_3-\alpha_2=$

The equation of the normal to the parabola $y^2 = 4ax$ at the point $\left( \frac{a}{m^2}, \frac{2a}{m} \right)$ is:

The normal at a point on the parabola $y^2=4x$ passes through $(5,0)$. If there are two more normals to this parabola passing through $(5,0)$,then the equation of one of these normals is

The normal at a point on the parabola $y^2=4x$ passes through $(5,0)$. If there are two more normals to this parabola which pass through $(5,0)$,the centroid of the triangle formed by the feet of these three normals is