Conic Sections Part 2

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• Dr Frost Slides 1-6

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• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 757a: Sketch an ellipse given its Cartesian equation. (not yet active)
• 757b: Write the parametric equations of an ellipse given its Cartesian equation, or vice versa. (not yet active)
• 757: Exam Practice: Ellipses and hyperbolae (excluding eccentricity)

Videos & Other Multimedia

How to Draw an Ellipse Using the Pin and String Method

Jesse Power 15184471

Foci of an ellipse | Conic sections | Algebra II | Khan Academy

Khan Academy Proving the string from foci works for an ellipse

Why slicing a cone gives an ellipse

Why slicing a cone gives an ellipse 3Blue1Brown

Enrichment Video

Why is there no equation for the perimeter of an ellipse‽

Stand-up Maths: Why is there no equation for the perimeter of an ellipse?

Online Platform

Tutorial Videos

3.2 Hyperbolas (FP1 – Chapter 3: Conic Sections 2)

3.2 Hyperbolas (FP1 – Chapter 3: Conic Sections 2) by Hinds Maths

A Level Further Maths | Further Pure 1 | Hyperbolas 🧮

A Level Further Maths | Further Pure 1 | Hyperbolas 🧮 by AJMaths

The Hyperbola – Loci (animation), Asymptotes, Cartesian and Parametric forms : ExamSolutions

The Hyperbola – Loci (animation), Asymptotes, Cartesian and Parametric forms : ExamSolutions by ExamSolutions

Conic sections: Intro to hyperbolas | Conic sections | Algebra II | Khan Academy

Conic sections: Intro to hyperbolas by Khan Academy

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• Dr Frost Slides 7-9

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 757c: Write the parametric equations of a hyperbola given its Cartesian equation, or vice versa. (not yet active)
• 757d: Sketch a hyperbola and give the coordinates of the roots and equations of the asymptotes. (not yet active)
• 757: Exam Practice: Ellipses and hyperbolae (excluding eccentricity)

Online Platform

Tutorial Videos

Ellipse – Equation of the directrix and coordinates of the focus : ExamSolutions Maths Revision

Ellipse – Equation of the directrix and coordinates of the focus : ExamSolutions Maths Revision by ExamSolutions

Conic Sections – Focus, Directrix and Eccentricity

Conic Sections – Focus, Directrix and Eccentricity by MasterWuMathematics

The Meaning of Eccentricity

The Meaning of Eccentricity by Eddie Woo

Determining Directrix from Equation of Ellipse

Determining Directrix from Equation of Ellipse by Eddie Woo

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• Dr Frost Slides 10-19

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 758a: Distinguish between a locus of points in the cases where the eccentricity e < 1, e = 1 and e > 1 (not yet active)
• 758b: Calculate the eccentricity for an ellipse with given Cartesian equation. (not yet active)
• 758c: Determine the coordinates of the foci and equations of the directrices for an ellipse with given Cartesian equation, where a > b (not yet active)
• 758d: Determine the coordinates of the foci and equations of the directrices for an ellipse with given Cartesian equation, where a < b (not yet active)
• 758e: Determine the a and b in the equation of an ellipse given a focus or directrix. (not yet active)
• 758f: Determine the coordinates of the foci and equations of the directrices for a hyperbola with given Cartesian equation. (not yet active)
• 758g: Show that the total distance from a point on an ellipse to the two foci is fixed. (not yet active)
• 758: Exam Practice: Eccentricity in ellipses and hyperbolae (not yet active)

Online Platform

Worksheets & Activities

• Alison Middelkoop Geogebra Exploring Eccentricity (original M. Agrata Abdullah)
• MadAsMaths (T. Madas)
  • Conic Sections Ellipse Q1–4, 6, 7, 12–15, 18, 20–22, 25, 26; Hyperbola Q1, 2, 5 (difficulty 2–5 of 5)

Tutorial Videos

Equation of a Tangent to an Ellipse (Cartesian form) : ExamSolutions Maths Revision

Equation of a Tangent to an Ellipse (Cartesian form) : ExamSolutions Maths Revision by ExamSolutions

A Level Further Maths | Further Pure 1 | Tangents and Normals to an Ellipse 🧮

A Level Further Maths by AJMaths

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• Dr Frost Slides 20-25

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 757e: Find an equation of a tangent to an ellipse. (not yet active)
• 757f: Find an equation of a normal to an ellipse. (not yet active)
• 757: Exam Practice: Ellipses and hyperbolae (excluding eccentricity)

Online Platform

Tutorial Videos

3.5 Tangents and normals to a hyperbola (FP1 – Chapter 3: Conic Sections 2)

3.5 Tangents and normals to a hyperbola (FP1 – Chapter 3: Conic Sections 2) by Hinds Maths

Finding the Equation of a Tangent Line to a Hyperbola

Finding the Equation of a Tangent Line to a Hyperbola by Larry Green

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• Dr Frost Slides 26-29

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 757g: Find an equation of a tangent to a hyperbola. (not yet active)
• 757h: Find an equation of a normal to a hyperbola. (not yet active)
• 757i: Find the equation of the tangent to a hyperbola which passes through a particular point. (not yet active)
• 757j: Determine an equation in terms of x where a generic line y = mx + c meets a hyperbola with given equation. (not yet active)
• 757: Exam Practice: Ellipses and hyperbolae (excluding eccentricity)

Worksheets & Activities

• MadAsMaths (T. Madas)
  • Conic Sections Rectangular Hyperbola Q14; Hyperbola Q4, 6, 8–10 (difficulty 3–5 of 5)

Tutorial Videos

A Level Further Maths | Further Pure 1 | Loci (Conic Sections 2) 🧮

A Level Further Maths | Further Pure 1 | Loci (Conic Sections 2) by AJMaths

Interesting Ellipse/Locus Question

Interesting Ellipse/Locus Question by Eddie Woo

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• Dr Frost Slides 30-34

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 759b: Determine the equation of the locus of the midpoint of the x and y intercepts of a tangent to an ellipse. (not yet active)
• 759d: Find an equation of the locus of the midpoint between a point on an ellipse and the foot of the perpendicular on a line x = k (not yet active)
• 759: Exam Practice: Loci problems involving parabolas, ellipses and hyperbolae

Worksheets & Activities

• MadAsMaths (T. Madas)
  • Conic Sections Ellipse Q23 (difficulty 5 of 5)

External Whole Topic Past Paper Style Questions

• WW Dr Frost Style QQQs Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)

Activities

• Math = Love (Sarah Carter)
  • Conic Cards Teaching Sequence
• Ben Sparks (GeoGebra)
  • Conic Sections Animated: GeoGebra

Worksheets

• Physics & Maths Tutor
  • FP1 Ch.3 Conic Sections 2: Questions by topic