(x-6)^2+(y-3)^2=25

2 min read Jun 17, 2024
(x-6)^2+(y-3)^2=25

Understanding the Equation: (x-6)^2 + (y-3)^2 = 25

The equation (x-6)^2 + (y-3)^2 = 25 represents a circle in the Cartesian coordinate system. Let's break down why this is the case and how to interpret the equation.

The Standard Form of a Circle Equation

The general standard form for the equation 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-6)^2 + (y-3)^2 = 25 to the standard form, we can identify the following:

  • Center: (h, k) = (6, 3)
  • Radius: r^2 = 25, so r = 5

Graphing the Circle

Now that we know the center and radius, we can easily graph the circle:

  1. Plot the center: Mark the point (6, 3) on the coordinate plane.
  2. Draw the circle: With the center as the starting point, use the radius (5 units) to draw a circle that passes through points 5 units away in all directions.

Key Takeaways

  • The equation (x-6)^2 + (y-3)^2 = 25 describes a circle with a center at (6, 3) and a radius of 5.
  • Understanding the standard form of a circle equation allows us to quickly identify the center and radius, making graphing and analyzing the circle simpler.
  • This equation represents an infinite set of points that are all equidistant (5 units) from the center point.

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