Help in making an animated locus is needed

Question

I have triangular cardboard ABC, right angled at C. As shown in the attached, initially, A and B are resting on the x- and y- axes respectively. A is then allowed to slide along the x-axis with B slides accordingly along the y-axis.

The locus of C has found to be:- $9x^2 – 16y^2 = 0$. But it needs to be shown in an animated form (in Geogebra if possible).

Considering I only have PASCAL programming experience, a detail explanation on how it is done is appreciated.

Answer 1

Here's what I tried in geogebra:

1. Create point $A$ on X-axis.
2. Make circle of radius $5$ centered at $A$.
3. Intersect the circle and Y-axis at point $B$.
4. Make angle of $53.13^\circ$ at $A$ and $36.87^\circ$ at $B$.
5. Intersect these angles at $C$.
6. Join line segments $AB$,$BC$ and $CA$ and hide everything else.
7. Trace on for point $C$.
8. Now just drag point $A$ on the X-axis.

Here are the results(The GIF is high quality so might take a couple seconds to load):

The locus of point $C$, as expected, is a straight line through origin with slope $\dfrac{3}{4}$. The other half of the locus is obtained when point $B$ is below the X-axis.