Equations of a Circle in Geometry
Equations of a Circle in Geometry
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Equations of a Circle in Geometry
What do you already know about the equations of a circle?
Learning Objective
At the end of the lesson you will be able to write and interpret the equation of a circle, understand its geometric meaning, and solve problems using examples.
What Is a Circle?
A circle is the set of all points in a plane that are a fixed distance from a given point. This fixed distance is called the radius, and the given point is the centre.
Main Elements of a Circle
Key elements: Centre (O), Radius (r), and any point (M) on the circle. The distance OM = r.
Standard Equation of a Circle
The standard equation: (x−a)^2 + (y−b)^2 = r^2, where (a, b) is the centre of the circle and r is the radius.
Example 1
Find the equation of a circle with centre at (3, 2) and radius 5. Solution: (x−3)^2 + (y−2)^2 = 25
General Equation of a Circle
The general form: x^2 + y^2 + Dx + Ey + F = 0. You can convert this equation to standard form by completing the square.
Practice Problem
Write the equation of a circle with centre at (0, 0) and radius 4. Try to solve, and we will discuss together in class.
Write down 3 things you learned in this lesson.
Write down 2 things you want to know more about.
Ask 1 question about something you haven't quite understood yet.
