Coordinate geometry

You will be able to

• Calculate the gradient, midpoint and length of AB, with the length as an exact surd, and write the equation of AB as y = mx + c, y − y₁ = m(x − x₁) and ax + by + c = 0.
• Determine the equation of the line through a point that is parallel (m₁ = m₂) or perpendicular (m₁m₂ = −1) to AB, and where the perpendicular meets AB.
• Deduce the equation of the perpendicular bisector of AB, including the cases where AB is horizontal or vertical.

You will be able to

• Determine the centre (−g, −f) and radius, r² = g² + f² − c, of a circle given in expanded form, and decide when the equation is not a circle.
• Calculate the equation of the tangent at a point of a circle from the gradient of the radius, using m₁m₂ = −1 and allowing for a vertical or horizontal radius.
• Deduce from b² − 4ac whether a line meets, touches or misses a circle, and find the tangent values of k.