Circle Inequalities (Graphing & Writing)

Описание: Ready to master circle inequalities? 🧐 In this video, Mario's Math Tutoring breaks down the equation of a circle and shows you how to use it to graph and write inequalities for circles!

We start by revisiting the definition of a circle as a set of equidistant points from a center, connecting it directly to the distance formula. You'll see how the standard equation of a circle ((x - h)² + (y - k)² = r²) is derived and how it forms the foundation for understanding circle inequalities.

Then, we dive into the core concept:

Greater than : Represents points outside the circle (further away from the center).
Less than: Represents points inside the circle (closer to the center).
Greater than or equal to: Includes points on the circle (solid line) and outside.
Less than or equal to : Includes points on the circle (solid line) and inside.
Watch as we tackle two clear examples:

Writing the circle inequality for a shaded region with a dashed line.
Graphing a given circle inequality ((x + 1)² + y² 4) and correctly shading the region.
By the end of this tutorial, you'll confidently graph and write circle inequalities, understanding the meaning behind dashed/solid lines and shaded regions!

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Timestamps:
00:00 Intro
0:13 What is the Equation of a Circle
0:40 How to Derive the Equation of a Circle
1:55 How to Write a Circle Inequality
2:40 Example 1 Write the Circle Inequality Given the Graph
3:29 Example 2 Graph (x+1)^2 + y^2 (greater than or equal to) 4

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