Pure 3. Coordinate Geometry

A Level Mathematics 9709 Examinations 2023 – 2025 Pure 1

Why do we study it?

• Circles are one of a collection of mathematical shapes called conics or conic sections.
• A conic section is a curve obtained from the intersection of a plane with a cone: ellipse, the parabola and the hyperbola. The circle is a special case of the ellipse.
• Conic sections provide a rich source of fascinating and beautiful results that mathematicians have been studying for thousands of years. Conic sections are very important in the study of astronomy. We also use their reflective properties in the design of satellite dishes, searchlights, and optical and radio telescopes.

1. Straight lines�--- midpoint

1. Straight lines – parallel and perpendicular lines

1. Straight Line: Equation

2. Equation Of A Circle

Some right angle facts

• If triangle ABC is right angled at B, then the points A, B and C lie on the circumference of a circle with AC as diameter.
• The perpendicular bisector of a chord passes through the centre of the circle.
• If a radius and a line at a point, P, on the circumference are at right angles, then the line must be a tangent to the curve.

3. Problems involving intersections of lines and circles