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MMathematicsPhysicsS6Conic sections

Conics lab: dishes, orbits and hyperbolas

A satellite TV dish, the orbit of a planet and a cooling tower are all cut from a cone. Explore their equations and their focus points.

▶ Start the lab🧠 Questions📄 My report
📡x² = 4fy · x²/a² + y²/b² = 1parabola, ellipse and hyperbola
LevelS6 (and A Level)
TimeAbout 35 min
You useFoci, eccentricity
PriceFree: no account

🎯 Aim

To investigate the equations and properties of conic sections.

You will learn to

  • Recognise the equations of the conics.
  • Find foci and eccentricity.
  • Find the asymptotes of a hyperbola.
  • Apply the focus property of a parabola.

🧭 What to do

  1. Choose Parabola and change the focal length: watch the rays meet.
  2. Choose Ellipse and change a and b: read the foci and e.
  3. Choose Hyperbola and read the asymptotes.
  4. Choose Circle.
  5. Answer the questions with the class data.
  6. Write your conclusion and download your lab report.

🔬 Lab bench

📋 The data

Equations and eccentricities.

🧠 Investigate: answer from the data

Type your answer and tap Check. Use 💡 Hint first; open the method only when you are stuck.

📄 My lab report

Your report collects the aim, your data table, the graphs, your answers and your conclusion. It is made on your phone or computer: nothing is sent to anyone.

Check your conclusion

A parabola x² = 4fy reflects rays parallel to its axis to the focus (0, f): this is why dishes work. An ellipse x²/a² + y²/b² = 1 has foci at ±c with c² = a² − b² and e = c/a < 1; a circle has e = 0. A hyperbola has c² = a² + b², e > 1 and asymptotes y = ±(b/a)x.

➕ Get more from this experiment

📝 Free

Print the worksheet (button above), download the data, and save your report. Teachers can project this page in class.

📦 Premium Lab Pack

1 000 RWF

  • Worksheet: draw an ellipse with two pins and a string; design a dish
  • Conic sections problems
  • Teacher guide and answer key
  • Exam-style questions with marking scheme
See the pack

👩‍🏫 For teachers

Use it as a practical when apparatus is missing, as homework, or as a project. Free lesson plans help you plan, teach and assess.

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