(x-3)^2+(y+5)^2=16

2 min read Jun 17, 2024

Understanding the Equation (x-3)^2 + (y+5)^2 = 16

The equation (x-3)^2 + (y+5)^2 = 16 represents a circle in the coordinate plane. Let's break down how to understand and interpret this equation.

The Standard Form of a Circle Equation

The general form of a circle's equation 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.

Analyzing the Given Equation

Comparing our equation, (x-3)^2 + (y+5)^2 = 16, with the standard form, we can identify the following:

Center: (h, k) = (3, -5)
Radius: r^2 = 16, therefore r = 4

Visualizing the Circle

Using this information, we can visualize the circle:

Locate the center: Plot the point (3, -5) on the coordinate plane.
Draw the radius: From the center, move 4 units in all directions (up, down, left, right) to mark points on the circle's circumference.
Connect the points: Draw a smooth curve connecting the points to represent the circle.

Conclusion

The equation (x-3)^2 + (y+5)^2 = 16 describes a circle with a center at (3, -5) and a radius of 4 units. Understanding the standard form of the circle equation allows us to easily identify its key characteristics and visualize its position and size on the coordinate plane.