Exam Techniques

Questions on coordinate geometry will be focused on the equations of lines and circles in a variety of forms, and may also require you to calculate lengths and areas. You should be able to derive these equations from information given in a wide range of formats, which may include coordinate points, gradients, intercepts or lengths. 

You may need to use the properties of parallel and perpendicular lines, and find their points of intersection.
 

You should be very familiar with the circle theorems given in the specification. It is often very helpful to use them to identify ‘hidden’ right angles (e.g. between tangents and a radius, or from the angle in a semi-circle, or from a radius bisecting a chord), as this will give you perpendicular lines to work with. They may also reveal clues about other shapes, such as similar triangles, which you can use.
 

In addition, remember that a tangent to a circle meets the circle at a single point, so if you substitute the equation of the tangent into the equation of the circle (giving another quadratic), then you know that the discriminant of this quadratic must be zero.
 

You should understand that the shortest distance between two lines is the perpendicular distance between them, and the shortest distance between a point and a line is the length of the perpendicular from the point to the line.​