Quick questions on Further coordinate systems: parabola, ellipse and hyperbola - Edexcel A-Level Further Maths

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are tangent gradient slips?

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For the parabola the gradient at parameter

t

\frac{1}{t}

; recompute it from

\frac{dy}{dx} = \frac{2a}{y}

rather than guessing.

What is wrong eccentricity relation?

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Use

b^2 = a^2(1 - e^2)

for the ellipse and

b^2 = a^2(e^2 - 1)

for the hyperbola; the sign inside the bracket differs.

What is q1?

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Write down a parametric point on the rectangular hyperbola

xy = 16

. [1 mark]

What is q2?

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State the focus and directrix of

y^2 = 12x

. [2 marks]

What is q3?

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Find the eccentricity of the ellipse

\frac{x^2}{16} + \frac{y^2}{7} = 1

. [3 marks]

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