Consider the following ellipse :

$\frac{x^2}{f\left(K^2+2 K+5\right)}+\frac{y^2}{f(K+11)}=1$, where $f(x)$ is a positive decreasing function. Then the value (values) of $K$ for which the major axis coincides with $x$-axis is

The equation $$\mathrm{r} \cos \theta=2 \mathrm{a} \sin ^2 \theta$$ represents the curve

A line of fixed length $$\mathrm{a}+\mathrm{b} . \mathrm{a} \neq \mathrm{b}$$ moves so that its ends are always on two fixed perpendicular straight lines. The locus of a point which divides the line into two parts of length a and b is

With origin as a focus and $$x=4$$ as corresponding directrix, a family of ellipse are drawn. Then the locus of an end of minor axis is