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# Coordinate Geometry in the (x,y) plane : Key Stage 5 (A2-Level) : Mathematics Content Knowledge

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Key Stage 5 (A2-Level)
Coordinate Geometry in the (x,y) plane
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# 1. How confident are you that you can write:

## Example

Example:
The Cartesian equation of the circle x2 + y2 = 52 can be written in terms of a third variable (called a parameter) as xr cos θ, yr sin θ.

Example:
The parametric equation of a curve is given by x = 3 – t2y = -2t. Write the equation in Cartesian form.

$y = - 2t \Rightarrow t = - \frac{y}{2}$

$x = 3 - t^2 = 3 - \left( { - \frac{y}{2}} \right)^2$

$= 3 - \frac{{y^2 }}{4}$

The Cartesian equation is y2 + 4x – 12 = 0.

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