# Space, shape and measurement: Use the Cartesian co-ordinate system to derive and apply equations

### Subject outcome

Subject outcome 3.1: Use the Cartesian co-ordinate system to derive and apply equations

### Learning outcomes

- Use the Cartesian coordinate system to derive and apply the equation of a circle (any centre).
- Use the Cartesian coordinate system to derive and apply the equation of a tangent to a circle given a point on the circle. Note that:
- Straight lines to be written in the following forms only: [latex]\scriptsize y=mx+c[/latex], [latex]\scriptsize y-{{y}_{1}}=m(x-{{x}_{1}})[/latex] and/or [latex]\scriptsize ax+by+c=0[/latex] (general form).
- Learners are expected to know and be able to use as an axiom ‘the tangent to a circle is perpendicular to the radius drawn to the point of contact.’

### Unit 1 outcomes

By the end of this unit you will be able to:

- Find the equation of a circle centred at the origin.
- Find the equation of a circle with centre [latex]\scriptsize (a,b)[/latex].
- Write the equation of the circle in standard form.

### Unit 2 outcomes

By the end of this unit you will be able to:

- Find the gradient of a tangent to a circle using analytical geometry.
- Find the equation of a tangent to the circle using analytical geometry.
- Find the equation of a tangent to a circle at the point of contact with the radius.