Finding the centre and radius

Finding the centre and radius

Understanding the Basics

• A circle in maths is defined based on its centre and radius.

• The centre of a circle is a fixed point which is equally distant from all points on the circumference.

• The radius is a line segment connecting the centre of the circle with any point on its circumference.

The Equation of a Circle

• The general form of a circle’s equation is (x - h)² + (y - k)² = r².

• In this equation, (h, k) denotes the centre of the circle and r represents the radius.

• This equation shows how every point in the circle is a specific distance (r) away from the centre.

Finding the Centre and Radius

• Identifying the centre of a circle from its equation involves determining the values of h and k. They are the coordinates of the centre of the circle.

• To find the radius, isolate r² in the circle’s equation, solve for r, then take the square root of the result. This will give the length of the radius.

Example Demonstrations

• If a circle’s equation is (x - 3)² + (y + 4)² = 36, the centre coordinates are (h=3, k=-4), and the radius is √36 i.e. 6.

• In the equation (x + 5)² + (y - 2)² = 25, the centre is at (-5, 2) and the radius is 5.

In Conclusion

• Understanding the relationship between the equation of a circle and its centre and radius is fundamental in algebra.

• Being able to identify these key components allows you to draw accurate representations of circles and solve various algebraic problems and scenarios. It’s a key skill in tackling geometry-related algebra problems.