We model the caustic curve formed by reflecting light from a point source in a circle. We ask ourselves this question: where does the central cusp lie?
Turn on the axes, draw a circle centered at the origin, and a point C on the y axis for the light source.
Define the radius of the circle, the distance of the light source from its center and the location of point B on the circumference.
Create a tangent at B and a line from C to B representing a light ray. Reflect it in the tangent.
Use the locus button to create the envelope of the reflected line as t varies
Put a point on the envelope curve and edit its location so its parameter is t.
Observe that this point lies at the point of tangency between the reflected line and the curve. What value of t would put the point at the cusp?
Edit the location of the point Type in pi/2
Open the symbolic panel Type in coordinates(D)
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