3. Coordinate systems – Edexcel Further Pure Mathematics 1 (FP1)

What students need to learn:
Cartesian equations for the parabola and rectangular hyperbola.
Students should be familiar with the equations:
\(y^2 = 4ax\) or \(x = at^2\) , \(y = 2at\) and
\(xy = c^2\) or \(x = ct\) , \(y = \dfrac{c}{t}\).

Idea of parametric equation for parabola and rectangular hyperbola.
The idea of \((at^2 , 2at)\) as a general point on the parabola is all that is required.

The focus-directrix property of the parabola.
Concept of focus and directrix and parabola as locus of points equidistant from focus and directrix.

Tangents and normals to these curves.
Differentiation of
\(y = 2a^{\frac{1}{2}}x^{\frac{1}{2}}\) , \(y = \dfrac{c^2}{x}\) .
Parametric differentiation is not required.

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