AS Mathematics₇₃₅₆

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.