Porisma
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Chapter exploration

Conic sections

Explore

Use the worked example below, then change one input or assumption. Predict which part of the answer must change before calculating.

Related interactive example

Explore this related example, then return to the prediction task above.

Squash, slide right, slide down

Three steps turn the wide ellipse into a circle of radius 3 centred at (4, −7).

Teal: C₁: x²/36 + y²/9 = 1. No comparison overlay.

Start: C₁: x²/36 + y²/9 = 1

The original ellipse: semi-axes 6 and 3, centred at the origin.

  • Shape at the selected step
  • Centre of the current shape
Ideas to try
  1. Which step makes the ellipse round? Why does only k=12k=\frac12 work?
  2. Check the equation of the final circle against the centre (4,−7)(4,-7).
Open the full interactive problem →
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