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(x-2)^2+(y+3)^2=16/9

3 min read Jun 17, 2024
(x-2)^2+(y+3)^2=16/9

Understanding the Equation: (x-2)^2 + (y+3)^2 = 16/9

The equation (x-2)^2 + (y+3)^2 = 16/9 represents a circle in the coordinate plane. Let's break down the equation and explore its meaning:

The Standard Form of a Circle

The general 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.

Analyzing Our Equation

Comparing our equation (x-2)^2 + (y+3)^2 = 16/9 with the standard form, we can identify the following:

  • Center: (h, k) = (2, -3)
  • Radius: r = √(16/9) = 4/3

Therefore, our equation describes a circle with its center at the point (2, -3) and a radius of 4/3 units.

Visualizing the Circle

To visualize the circle, you can follow these steps:

  1. Plot the center: Locate the point (2, -3) on the coordinate plane.
  2. Draw the radius: From the center (2, -3), draw a line segment of length 4/3 units in all directions (up, down, left, right).
  3. Connect the points: Connect the endpoints of these radius segments to form a smooth circle.

Key Points

  • The equation (x-2)^2 + (y+3)^2 = 16/9 is a concise representation of a circle with specific properties.
  • By understanding the standard form of a circle's equation, you can quickly identify its center and radius.
  • Visualizing the circle on a coordinate plane helps to understand its geometrical properties.

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