Recognising Conics

From equation to curve

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Same-sign squares: ellipse (or circle). Opposite signs: hyperbola. One square: parabola.
• Complete the square to find the centre.
• Circle: $(x - h)^2 + (y - k)^2 = r^2$.

Steps

1. Read the squares
2. Name it
3. Tune the coefficients
4. Where are the foci?
5. Area of an ellipse
6. Find the centre