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We take the family of ellipses with foci (a,0), (-a, 0) whose generic member we pass through the point (0,t). We look at the locus of the points of i...
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Again, we can force the tangency by reflecting one focus in the tangent line and joining the reflection to the other focus, then intersecting the resu...
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Given a triangle and a point lying on a circle concentric with the circumcircle but with twice the area, we create another triangle by reflecting the ...
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There are a family of conics that go through four points; the fifth point defines one conic. One way to determine this conic is to first make a family...
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Take a general equation, and look at the locus of midpoints of chords parallel to the y axis.
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Given a point on the conic, we create the line joining the opposite ends of the two focal chords. We examine its envelope, which is an ellipse, as w...
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Where does the normal intersect the minor axis?
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We contruct conjugate diameters. The triangle formed by the conjugate radii and the line connecting the tangecy points has constant area.
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