(x-1)^2+(y+2)^2=9

3 min read Jun 17, 2024

Exploring the Circle: (x-1)^2 + (y+2)^2 = 9

This equation represents a circle in the standard form. Let's break down its components and understand what it tells us about the circle:

Standard Form of a Circle

The standard 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

Decoding the Equation: (x-1)^2 + (y+2)^2 = 9

Comparing this equation with the standard form, we can extract the following information:

Center: (h, k) = (1, -2)
Radius: r^2 = 9, so r = 3

Therefore, the equation (x-1)^2 + (y+2)^2 = 9 defines a circle with a center at (1, -2) and a radius of 3 units.

Visualizing the Circle

To visualize the circle, follow these steps:

Plot the center: Mark the point (1, -2) on the coordinate plane.
Draw the radius: From the center, draw a line segment of length 3 units in any direction. This represents the radius.
Complete the circle: Using the radius as a guide, draw a circle that passes through the end point of the radius and is centered at (1, -2).

Key Points

The equation (x-1)^2 + (y+2)^2 = 9 describes a specific circle.
The center and radius of the circle can be directly identified from the equation.
Understanding the standard form of a circle's equation allows us to quickly analyze its properties.

This equation provides a compact and efficient way to represent a circle, making it easier to analyze and manipulate in various geometric and algebraic applications.