A-level Mathematics₇₃₅₇

Understand and use the equation of a straight line, including the forms $\mathit{y}\mathsf{-}{\mathit{y}}_{\mathsf{1}}\mathsf{=}\mathit{m}\left(\mathit{x}\mathsf{-}{\mathit{x}}_{\mathsf{1}}\right)\mathit{}\begin{array}{cc}& \\ & \end{array}\mathsf{a}\mathsf{n}\mathsf{d}\begin{array}{cc}& \\ & \end{array}\mathit{a}\mathit{x}\mathsf{+}\mathit{b}\mathit{y}\mathsf{+}\mathit{c}\mathsf{=}\mathsf{0}$ ; gradient conditions for two straight lines to be parallel or perpendicular.

Be able to use straight line models in a variety of contexts.

Understand and use the coordinate geometry of the circle including using the equation of a circle in the form ${\mathsf{(}\mathit{x}\mathsf{-}\mathit{a}\mathsf{)}}^{\mathsf{2}}\mathsf{+}{\mathsf{(}\mathit{y}\mathsf{-}\mathit{b}\mathsf{)}}^{\mathsf{2}}\mathsf{=}{\mathit{r}}^{\mathsf{2}}$ ; completing the square to find the centre and radius of a circle; use of the following properties:

• the angle in a semicircle is a right angle
• the perpendicular from the centre to a chord bisects the chord
• the radius of a circle at a given point on its circumference is perpendicular to the tangent to the circle at that point.

Understand and use the parametric equations of curves and conversion between Cartesian and parametric forms.

Use parametric equations in modelling in a variety of contexts.