Show that the absolute value of difference of the focal distances of any point $P$ on the hyperbola is the length of its transverse axis.

Identify the type of conic and find centre, foci, vertices, and directrices of the curve $\frac{{\left(x-3\right)}^2}{225}+\frac{{\left(y-4\right)}^2}{289}=1$.

Identify the type of conic and find centre, foci, vertices, and directrices of the curve $\frac{{\left(x+1\right)}^2}{100}+\frac{{\left(y-2\right)}^2}{64}=1$.

Identify the type of conic and find centre, foci, vertices, and directrices of the curve $\frac{{\left(x+3\right)}^2}{225}-\frac{{\left(y-4\right)}^2}{64}=1$.

Identify the type of conic and find centre, foci, vertices, and directrices of the curve $\frac{{\left(y-2\right)}^2}{25}-\frac{{\left(x+1\right)}^2}{16}=1$.

Identify the type of conic and find centre, foci, vertices, and directrices of the curve $18x^2+12y^2-144x+48y+120=0$.

Identify the type of conic and find centre, foci, vertices, and directrices of the curve $9x^2-y^2-36x-6y+18=0$.