Intersecting a circle with a cubic locus curve, mostly
I created two applets where I need to intersect a circle (circumscribed to triangle ABC there) with a cubic locus curve (orange color - created by me as the locus of the intersection points of all tangents from two points P and Q to all parabolas inscribed in triangle ABC).
If a locus curve is (functionally) just as with any other curve offered by GeoGebra (lines and conics, at least), then I should be able to use the "Intersect" command/Icon in order to obtain the intersection points - but when I try nothing happens!
Or is it that the curves needing to be intersected have to be of degrees one or two only (hence cubics won't be dealt with) ?
Further, I saw no "value" (i.e., equation) displayed for the cubic created: should GeoGebra not be able to assess that no transcendental function had been used, hence the resulting locus should be an algebraic curve, whose equation should then be determined, even when the degree would not be discernible ?
Same problem when I created quartics: no equation is displayed:
Going back to the cubics and their intersection with the circumcircle ABC: I had to "fake" their intersection, by attaching a point to one of the curves, then manually sliding that point along its curve path until the "intersection position" (visually) appears to be attained. In the second picture involving cubics, the intersection point F lies quite far from its correct intersection point position, between the cubic and the circle. I have manually corrected that (more than once!), but after I save it all, point F is still astray! Fortunately, I noticed that the "Refresh" button on the applet would bring point F in a correct position, but ... why should it not have been saved correctly there in the first place ? I had to put a message for users/viewers to first refresh the image ...
Finally: should GeoGebra not offer, along with its "Conic through five points" tool, the dual tool too ? That would be: "Conic tangent to five lines". There is quite a bit of work constructing it. I know I could simply create this tool myself, for my own use, but ... past attempts have shown that design flaws caused some of my tool to fail, at least in certain configurations (choice of initial data).