Conic sections - locus, eccentricity, focus, directrix

The parabola, ellipse and hyperbola can each be defined using the concepts of locus and eccentricity.

See p93 QMaths12C.

A parabola is the locus of a point which moves so that its distance from a fixed point (the focus) is the same as its distance from a fixed line (the directrix) i.e. the eccentricity is 1.

On the grid paper provided, mark the focus at the centre of the circles and choose one of the lines as the directrix. Now use the circles and lines to help you mark points on the parabola. Repeat the process for the directrix drawn in different places. What happens to the shape of the parabola as the distance between the focus and directrix increases?

On another copy of the grid paper, mark the focus and mark a directrix distance 6 units from the focus. Draw the conic sections with eccentricity 1, ½ and 2 (parabola, ellipse, hyperbola).