(x-3)^2+(y+2)^2=9

3 min read Jun 17, 2024

Understanding the Equation: (x - 3)^2 + (y + 2)^2 = 9

The equation (x - 3)^2 + (y + 2)^2 = 9 represents a circle in the Cartesian coordinate system. Let's break down why:

The Standard Form of a Circle

The standard form of 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.

Analyzing Our Equation

Comparing our equation (x - 3)^2 + (y + 2)^2 = 9 with the standard form, we can deduce:

Center: The center of the circle is at the point (3, -2). This is because the equation is in the form (x - h)^2 + (y - k)^2, and h = 3 and k = -2.
Radius: The radius of the circle is 3. This is because the right-hand side of the equation is equal to 9, which is the square of the radius (r^2 = 9, therefore r = 3).

Visualizing the Circle

To visualize this circle, you can plot the center point (3, -2) on a graph. Then, draw a circle with a radius of 3 units around this center point. This will give you a clear visual representation of the equation (x - 3)^2 + (y + 2)^2 = 9.

Key Takeaways

The equation (x - 3)^2 + (y + 2)^2 = 9 describes a circle centered at (3, -2) with a radius of 3.
Understanding the standard form of a circle equation allows you to quickly identify the center and radius of any given circle.
Visualizing the circle on a graph helps to solidify your understanding of the equation.