The length of the latus rectum of the ellipse is 16x² + 25y² = 400 is

The equation 8x² + 12y² $$-$$ 4x + 4y $$-$$ 1 = 0 represents

The minimum length of intercept on any tangent to the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ cut by the circle $x^2+y^2=25$ is

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