UNIT OVERVIEW

In this unit, you will combine algebra and geometry to study circles in the Cartesian plane. You already know how to work with straight lines, gradients, and the distance formula. Now you will use those skills to write equations for circles, find tangent lines, and solve problems involving both.

What you will learn:

• Write the equation of a circle in standard form and general form
• Find the centre and radius from any circle equation
• Determine whether a point lies inside, on, or outside a circle
• Understand that a tangent is perpendicular to the radius at the point of tangency
• Find the equation of a tangent to a circle at a given point
• Solve problems involving circles and tangent lines

Why this matters:

Circle equations are used in GPS systems (to find your location from satellite signals), in designing roundabouts and roads, and in medical imaging where scanners rotate in circular paths.

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