Coordinate geometry

Straight LinesSign up

understand and use the equation of a straight line in the forms y = mx + c, y - y1 = m(x - x1) and ax + by + c = 0 · be able to calculate the gradient of a line through two points and the distance between two points · be able to find the midpoint of a line segment and the coordinates of the point dividing it in a given ratio

Parallel and Perpendicular LinesSign up

understand the conditions for two lines to be parallel (equal gradients) or perpendicular (product of gradients = -1) · be able to find the equation of a line parallel or perpendicular to a given line through a specified point

The Equation of a CircleSign up

understand and use the equation of a circle (x - a)^2 + (y - b)^2 = r^2, including completing the square to find the centre and radius from a general second-degree form

Lines and Circles, and the Intersection of a Line and a CurveSign up

be able to find equations of tangents and chords to a circle and solve problems using the perpendicularity of a tangent to the radius at the point of contact · understand and use the standard circle theorems: angle in a semicircle, perpendicular from centre bisects chord, tangent perpendicular to radius