Let the line $x-y+1=0$ intersect the circle $x^2+y^2+2 x+2 y+1=0$ in two points $A$ and $B$. If $A B$ is the diameter of the circle $x^2+y^2+2 g x+2 f y+c=0$, then $g+f=$

If the focal distance of a point $P\left(2, y_1\right)$ on the parabola $y^2=k x$ is 3 , then the equation of the tangent drawn at $P$ to the given parabola is

Normals are drawn from the point $P(8,0)$ to the parabola $y^2=12 x$. If $\theta$ is the acute angle between two non-horizontal normals among them, then $\tan \theta=$

Let $S$ and $S^{\prime}$ be the foci of an ellipse $E$ and $B$ be one end of its minor axis. Let $\angle S^{\prime} S B=\pi / 6$ and $(2 \sqrt{3}, 1)$ be a point on $E$. If $X$-axis is the major axis and $Y$-axis is the minor axis of the ellipse $E$, then the sum of the squares of the lengths of major and minor axis is