# Conic Sections

## The Nephoid – a caustic in a coffee cup

The Nephoid is the curve formed by the envelope of rays reflected on a circular surface from a set of initial parallel rays.  In other words, the curve which owns all the rays as tangents. The geomtery of each ray path is relatively straight forward, involving properties of parallel lines and isocelels triangles. It is …

## Conic sections in the sand give shipwrecked philosophers good hope

Conic sections in the sand give shipwrecked Socratic philosopher, Aristippus, good hope. I wonder if this ancient tale, in which the mathematics of planetary motion some 2000 years prior to it’s application in space travel, is used to signify the presence of intelligent life and therefore hope of salvation has some echo in our …

## Further Maths Conic Section Locus Problem

Intersection of perpendicular normals on one parabola makes another. Another A level further maths conic sections locus problem.

## Conic Sections Tangent/Normal Locus

A level further mathematics question animated.  Mid point of Normal x-intercept and Tangent y-intercept traces out another curve as original point moves round an ellipse.

## Hyperbola – Focus Directrix

Hyperbola – locus of points in which ratio of distance from a focus point to the perpendicular distance to a line (directrix) is constant and greater than 1.  Staple diet of school Further Mathematics.