For a second generalization of the WALLACE-lines we look for the other intersection points of the perpendicular lines to the sides of the triangle ABC through a point X with the sides of this triangle ABC called P', Q', R' and P'', Q'', R''. Now we ask for the locus of X while the points P', Q', R' or the points P'', Q'', R'' are collinear.
By algebraic considerations we find out, that this locus consists of two conics. One for the collinearity of [P'Q'R'] called the WALLACE-right-conic c' and the other one for the collinearity of [P''Q''R''] called the WALLACE-left-conic c''.
With CINDERELLA we can create each one, if we have five points which lie on the conic.
In the interactive exercise 2 we look for such points on the WALLACE-right-conic c':

First we move the point X to get an idea for the solution. After a while we can see that the intersection point of the perpendicular lines of the line AB through the point B and the line BC through the point A is one of these points. By cyclic permutation we get three special points. Of course, the points A, B, C lie on the conic, too.
Alternatively, we can do this exercise as well by clicking the "Questionmark Button" in the toolbar.