2%2B(y%E2%88%9210)2%3D169.jpeg "(x+4)2+(y−10)2=169")
Understanding the Equation: (x+4)² + (y-10)² = 169
This equation represents a circle in the Cartesian coordinate system. Let's break down why:
The Standard Form of a Circle Equation
The standard form of a circle's equation is:
(x - h)² + (y - k)² = r²
Where:
- (h, k) represents the center of the circle.
- r represents the radius of the circle.
Analyzing our Equation
Comparing our equation (x+4)² + (y-10)² = 169 to the standard form, we can identify:
- Center (h, k): (-4, 10)
- Radius (r): √169 = 13
Interpreting the Results
This means our equation represents a circle with:
- Center: Located at the point (-4, 10) on the coordinate plane.
- Radius: Measuring 13 units.
Visualizing the Circle
You can visualize this circle by plotting the center (-4, 10) and then drawing a circle with a radius of 13 units around it.
Key Takeaways
Understanding the standard form of a circle equation allows us to quickly determine its center and radius, making it easier to visualize and work with circles in various applications.