Equation of Circle Game

Equation of Circle Game
In this game, you are tasked with mastering the geometry of orbits. To succeed, you must understand the relationship between a circle on a coordinate plane and its algebraic equation: (x - h)² + (y - k)² = r². Scroll down the page for a more detailed explanation.
 

 

How to Play the Equation of Circle Game
Mission Modes

1. Visual Scan (Identify Mode)
   In this mode, you are shown a circle on a grid. Your job is to select the correct equation that represents it.
   Locate the Center (h, k): Look for the green dot in the middle.
   Measure the Radius (r): Count how many grid units it is from the center to the edge.
   Check the Equation: Remember, the signs in the equation are opposite to the coordinates. If the center is at (2, -3), the equation will look like (x - 2)² + (y + 3)².
   

2. Center/Radius Recon (Properties Mode)
   Here, you are given an equation (e.g., (x + 1)² + (y - 5)² = 9) and must pick the correct properties from the list.
   Extract Center: Flip the signs inside the parentheses.
   Extract Radius: Take the square root of the number on the far right (the constant).
   

3.Advance & Progress
Click “NEXT SECTOR ➜” to move to the next challenge. Watch the progress bar at the top to see how close you are to completing the mission.

Controls & Exit
Score: Your “Data Packets” are tracked in the top right corner.
Abort Mission: If you need to switch modes or restart, click the “Abort Mission (Exit)” button at any time to return to the main menu.
Mission Complete: After 10 questions, you will receive a final accuracy report. Click “RETURN TO HQ” to start a new round.

The Equation of Circle
The Standard Form
The standard equation of a circle is:
(x - h)² + (y - k)² = r²
Where:
(h, k) is the coordinate of the center of the circle.
r is the radius (the distance from the center to the edge).
(x, y) represents any point on the boundary of the circle.

How it Works (The Logic)
If you pick any point (x, y) on the circle and draw a right triangle connecting it to the center (h, k):
The horizontal distance (the base of the triangle) is (x - h).
The vertical distance (the height of the triangle) is (y - k).
The hypotenuse is the radius r.
According to the Pythagorean Theorem (a² + b² = c²), the relationship is:
(x - h)² + (y - k)² = r²

The video gives a clear, step-by-step approach to learn the equation of a circle.

• Show Video

 

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