Hyperbolas

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We contruct conjugate radii and project them onto the hyperbola axis. The areas formed by the two triangles are the same.
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If a rectangular hyperbola circumscribes a triangle, it will also pass through the orthocenter of the triangle. A rectangular hyperbola has asymptotes...
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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.
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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.
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If a rectangular hyperbola circumscribes a triangle, the center of the hyperbola lies on the 9 point circle of the triangle.
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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 ...
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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, ...
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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...
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