# Coordinate systems – Edexcel FP1

#### 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.