Let $l$ be the directrix of the parabola $9y^2+12y+9x-14=0$ and $l_1$ be the line passing through the vertex of this parabola and the origin. If $(h, k)$ is the point of intersection of $l$ and $l_1$,then $h+k=$

The equation ${y^2} - 2x - 2y + 5 = 0$ represents:

If $PQ$ is a focal chord of the parabola $y^2=4x$ with focus $S$ and $P=(4,4)$,then $SQ=$

$A$ pair of tangents is drawn from an external point $P$ to the parabola $y^2 = 4x$. If $\theta_1$ and $\theta_2$ are the angles made by the tangents with the $x$-axis such that $\theta_1 + \theta_2 = \frac{\pi}{4}$,find the locus of $P$.

If two normals to the parabola $y^2 = 4x$ passing through the point $(15, 12)$ are $4x + y = 72$ and $3x - y = 33$,find the third normal.

$A$ point on the parabola whose focus is $S(1,-1)$ and whose vertex is $A(1,1)$ is