If the vertex of the conic $y^{2}-4y=4x-4a$ always lies between the straight lines $x+y=3$ and $2x+2y-1=0$, then:

Let the equation of the tangent at a point $P$ on the parabola $x^2-4x-4y+16=0$ be $2x-y-5=0$. If the equation of the normal drawn at $P$ to this parabola is $ax+y+c=0$,then find the value of $ac$.

The locus of the midpoint of the chord of the parabola $y^2 = 4ax$ which subtends a right angle at the vertex is

If the distances of two points $P$ and $Q$ on the parabola $y^2 = 4ax$ from its focus are $4$ and $9$ respectively,then what is the distance of the point of intersection of the tangents at $P$ and $Q$ from the focus?

If a normal to the parabola $y^2=12x$ at $A(3,-6)$ cuts the parabola again at $P$,then the equation of the tangent at $P$ is

If the line $3x - 2y + 12 = 0$ intersects the parabola $4y = 3x^2$ at the points $A$ and $B$,then at the vertex of the parabola,the line segment $AB$ subtends an angle equal to