The line $l x+m y+n=0$ will touch the parabola $y^2=4 a x$, if $\mathrm{In}=a m^2$.

If $P$ is a point on the ellipse $\frac{x^2}{16}+\frac{y^2}{25}=1$ whose foci are $S$ and $S^{\prime}$, then $P S+P S^{\prime}=8$.

The line $2 x+3 y=12$ touches the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=2$ at the point $(3,2)$.

The locus of the point of intersection of lines $\sqrt{3} x-y-4 \sqrt{3 k}=0$ and $\sqrt{3} k x+k y-4 \sqrt{3}=0$ for different value of $k$ is a hyperbola whose eccentricity is 2 .

The equation of the circle having centre at $(3,-4)$ and touching the line $5 x+12 y-12=0$ is ............. .