Let $L$ be a normal to the parabola $y^2=4x$. If $L$ passes through the point $(9,6)$,then $L$ is given by
$(A)$ $y-x+3=0$ $(B)$ $y+3x-33=0$ $(C)$ $y+x-15=0$ $(D)$ $y-2x+12=0$

If the line $x-y=-4K$ is a tangent to the parabola $y^2=8x$ at $P$,then the perpendicular distance of the normal at $P$ from $(K, 2K)$ 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:

If $(a, b)$ is the midpoint of a chord passing through the vertex of the parabola $y^2 = 4x$,then:

If $ax^2+2hxy+by^2-82x+98y+144=0$ is the equation of a parabola with focus $(2,-3)$ and directrix $3x-2y+5=0$,then $ax^2+2hxy+by^2=0$ represents

For the parabola $y^{2} = 4x$,the point $P$ whose focal distance is $17$ is