Parabolas

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The caustic curve (or catacaustic) is the envelope of a family of reflected rays. If a set of rays parallel to the axis of a parabola is reflected in...
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We take the family of parabolas with foci (0,0), whose generic member we pass through the point (0,-b). We look at the locus of the points of interse...
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If m is a quarter of the parameter of a parabola, and u and v are the lengths of two perpendicular tangents, we are to show that u^(2/3)/v^(4/3) + v^(...
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We find the intersection of two tangents to a parabola.
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We take the points at x locations x_0, x_0+h/2, and x_0+h on the curve Y=X^2, and we create triangles by connecting the points and their tangents. Not...
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If we create a parametric curve where both x and y are quadratic in t, and inspect its implicit equation, we see that it is a conic.
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