

We contruct conjugate radii and project them onto the hyperbola axis. The areas formed by the two triangles are the same.



If a rectangular hyperbola circumscribes a triangle, it will also pass through the orthocenter of the triangle. A rectangular hyperbola has asymptotes...



If two lines have the equations A(x,y)=0 and B(x,y)=0, then the conic AB=a is a hyperbola with A and B as asymptotes.



The area of the triangle whose vertices are the center of the hyperbola and the intersections of a tangent line with the asymptotes is constant.



If a rectangular hyperbola circumscribes a triangle, the center of the hyperbola lies on the 9 point circle of the triangle.



We take a point and a constrained subtended angle on a horizontal line. The locus of the center of the circumcircle of the resulting triangle forms a ...



For a given ellipse, we take the tangents through a fixed point. We take the midpoint of the segment of a general tangent cut off by these tangents, ...



To generate area k, we use one short side length a, the other length 2k/a. Clearly the locus is a hyperbola. We can find its foci by drawing a hyperb...



