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LearnEdexcel9FM0First teaching 2017Option · Further Pure Mathematics 1Conic sections

Option · Module

Conic sections

2 subtopics≈ 95 min in total

Start the module: Parabola and rectangular hyperbola Open graphing calculator

Parabola and rectangular hyperbola
The parabola $y^2=4ax$ is every point equidistant from the focus $(a,0)$ and the directrix $x=-a$ ; parametrically $(at^2,2at)$ . The rectangular hyperbola $xy=c^2$ has parametric form $\left(ct,\frac ct\right)$ . Parameters make tangents and normals tidy.
≈ 45 min
Ellipse and hyperbola
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is an ellipse with $b^2=a^2(1-e^2)$ ; $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is a hyperbola with $b^2=a^2(e^2-1)$ . Both have foci $(\pm ae,0)$ and directrices $x=\pm\frac ae$ ; distance to a focus is $e$ times distance to the matching directrix.
≈ 50 min