Ellipse with customizable size, position, rotation, color

I really had a lot of trouble figuring ellipses out, especially with rotation – so wanted to share.
This works, but I don’t really understand it! If you know more about this stuff, please comment improvements that could be made.

Used these two things to figure it out:
https://www.shadertoy.com/view/wclGW2
https://godotshaders.com/shader/simple-ellipse-shader/

To use it, create a new ShaderMaterial on a canvas item such as a ColorRect or a TextureRect with a PlaceholderTexture2D or similar.

Have a look at my profile for further iterations such as randomized variables, and generating more than one at a time.

Shader code

shader_type canvas_item;

uniform float rotation: hint_range(0.0, 360.0) = 0.0;
uniform float posX: hint_range(0.0, 1.0) = 0.5;
uniform float posY: hint_range(0.0, 1.0) = 0.5;
uniform float height: hint_range(0.0, 1.0) = 0.5;
uniform float width: hint_range(0.0, 1.0) = 0.5;
uniform vec4 ellipseColor: source_color = vec4(1.0, 0.0, 0.0, 1.0);

void fragment() {
	// Idk the math, but it works
	float angle = 1.0 * (radians(rotation / 2.0) * 1.0);
	// This line sets the background. Delete it to make transparent or edit to make different color
	COLOR = vec4(0.0, 0.0, 0.0, 1.0);
	vec2 pos = vec2(posX, posY);
	
	// Don't even ask, took the below from - https://www.shadertoy.com/view/wclGW2
	float theta = angle * 2.0; // Ellipse orientation
	mat2 rot = mat2(vec2(cos(theta), -sin(theta)), vec2(sin(theta), cos(theta)));
	vec2 localCoord = rot * (UV - pos);
	float dist = pow(localCoord.x / (width / 2.0), 2.0) + pow(localCoord.y / (height / 2.0), 2.0);
	
	// It works
	if (floor(dist) < 0.1){
		COLOR = mix(ellipseColor, vec4(0.0, 0.0, 0.0, 1.0), floor(dist));
	}
}