# Compute Parabolic coordinates-related properties

Parabolic coordinates form an orthogonal system, which simplifies the representation of geometric shapes like parabolas and enables straightforward calculations for vector operators due to their identical scale factors.

### :clapper:the orthogonal grid formed by the intersecting parabolas

> The demo provides a visual proof that the two families of parabolas always intersect at a right angle. It also shows that the position vector is a direct line from the origin to any point in space, with its components defined by the coordinate system's conversion formulas.

{% embed url="https://youtu.be/NgKc0dSSMFU" %}

### :pen\_ballpoint:Mathematical Proof

{% embed url="https://viadean.notion.site/Compute-Parabolic-coordinates-related-properties-2591ae7b9a3280afb2d2d8d9a9948ab3?source=copy_link" %}
