Conic Sections

What the page covers

The unit brings together the four main curves: the parabola, the circle, the ellipse and the hyperbola. Most of the material is mind maps, and the majority of those focus on parabolas. You will also find flashcard decks, slide sets, flowcharts, notes and a few quizzes.

Where to start

Begin with the mind map Conic sections. It lays out the equation forms side by side: y=a(x-h)2 +k and x= a(y-k)2 +h for parabolas, the circle form (x-h)2+(y-k)2=r2, and the horizontal and vertical forms for ellipses and hyperbolas.

Next, open the notes called Conics. They explain how cutting a cone at different angles gives a parabola, an ellipse or a circle.

Going deeper on parabolas

1. Read one of the mind maps called Parabolas. They define a parabola as a curve where every point is equally far from a focus and a directrix, and they cover the vertex and the axis of symmetry.
2. Check the mind map Conic Sections Formulas for the forms with a vertical or horizontal axis.
3. Use the mind map Conics to see the parts of each curve, such as focus, directrix, vertex and latus rectum.

Practising

The flashcard deck Conic Sections asks you to match equations to graphs, for example the parabola (x − 2)^2 = 12(y − 3). Other decks include Transformations of conics and Locus and the parabola. The slide sets Conic Questions and Conic Intersection Questions give more problems to work through.

Then try the quizzes Equations of Circles & Ellipses and U4 T1 Conic Sections Review. Use the maps to check any answer you got wrong, then go back to the quiz.

Where it fits

This unit sits in the Functions and Graphs strand of Mathematics. Teachers can pick a map or deck to set as revision. Students can open any resource now, then make their own version of a favourite map.