The equation of the ellipse with foci at $(0,\pm 4)$ and vertices at $(0,\pm 7)$ is $\frac{x^2}{16}+\frac{y^2}{49}=1$.

The length of the latus rectum of the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1\text{ and }\frac{(x+2{)}^2}{4}+\frac{(y-1{)}^2}{9}=1$ are equal.

The equation of the latus recta of the ellipse $\frac{(x-4{)}^2}{16}+\frac{(y-1{)}^2}{9}\text{ are }x=4\pm \sqrt{7}$.

The line $y=x+2$ is a tangent to the ellipse $\frac{x^2}{2}+\frac{y^2}{1}=1$.

The conjugate axis of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ meets the hyperbola at two points which are at a distance $2b$ from each other.

The conjugate axis of the hyperbola $\frac{(y-3{)}^2}{9}-\frac{(x+2{)}^2}{3}=1$ is parallel to the line $x=4$.

The length of the transverse axis of the hyperbola with foci at$(\pm 5,0)$ and vertices at $(\pm 2,0)$ is $10$. 

The length of the latus recta of the hyperbola $\frac{x^2}{25}-\frac{y^2}{16}=1$ and $-\frac{x^2}{16}+\frac{y^2}{25}=1$ are equal.

The $y-$axis is tangent to the hyperbola $a{y}^2-b{x}^2=1$.