How to write this conic equation in standard form? $$x^2+y^2-16x-20y+100=0$$
Standard form? Circle or ellipse?

$$
\begin{align} 
x^2+y^2-16x-20y+100 & = 0 \\ \\
\color{blue}{\bf x^2 -16x} + \color{red}{\bf y^2 -20y } + 100 & = 0
\end{align}
$$
We complete the square: $$x^2+bx+(b/2)^2-(b/2)^2+c= (x+b/2)^2+c-(b/2)^2$$
$$\begin{align}
\color{blue}{\bf x^2 - 16x} + \underbrace{\bf \left(\frac{-16}{2}\right)^2}_{\color{green}{\bf \large +64}} + \color{red}{\bf y^2 - 20y} + \underbrace{\bf \left(\frac{-20}{2}\right)^2}_{\color{green}{\bf \large + 100}} + 100 {\color{green}{\bf - 64 -100}} & = 0 \\ \\
(x^2 - 16x + 64) + (y^2 - 20 y + 100) - 64 & = 0\\ \\
(x - 8)^2 + (y - 10)^2 - 64 & = 0\\ \\
(x - 8)^2 + (y - 10)^2 & = 64 = (8)^2 \\
\end{align}
$$
The equation of a circle with center $(a, b)$ and radius $r$ is given by $$(x - a)^2 + (y - b)^2 = r^2$$
In your case, we have a circle centered at $(8, 10)$ with radius $r = 8$.
