%5E2%2B(y-4)%5E2%3D25.jpeg "(x-3)^2+(y-4)^2=25")
Understanding the Equation: (x-3)^2 + (y-4)^2 = 25
This equation represents a circle in the Cartesian coordinate system. Let's break down how to understand its properties:
The Standard Form of a Circle's Equation
The general equation for a circle is: (x - h)^2 + (y - k)^2 = r^2
Where:
- (h, k) represents the center of the circle.
- r represents the radius of the circle.
Identifying the Center and Radius
In our given equation, (x - 3)^2 + (y - 4)^2 = 25, we can directly identify the center and radius:
- Center: (h, k) = (3, 4)
- Radius: r^2 = 25, so r = 5
Therefore, this equation describes a circle with a center at (3, 4) and a radius of 5 units.
Visualizing the Circle
To visualize this circle, you can:
- Plot the center: Mark the point (3, 4) on a coordinate plane.
- Draw the circle: Using the radius of 5 units, draw a circle around the center point.
Key Takeaways
- The equation (x-3)^2 + (y-4)^2 = 25 describes a circle.
- The center of the circle is located at (3, 4).
- The radius of the circle is 5 units.
By understanding the standard form of the circle equation and its components, you can readily identify the center and radius of any circle represented by such an equation.