(x-5)2+(y-6)2=81

2 min read Jun 17, 2024
(x-5)2+(y-6)2=81

Understanding the Equation: (x-5)^2 + (y-6)^2 = 81

This equation represents a circle in the standard form. Let's break down the components and understand its significance:

Standard Form of a Circle:

The general equation for 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.

Applying it to our equation:

In our case, we have: (x - 5)^2 + (y - 6)^2 = 81

Comparing this to the standard form, we can identify:

  • Center (h, k): (5, 6)
  • Radius (r): √81 = 9

Interpretation:

This equation describes a circle with a center at the point (5, 6) and a radius of 9 units.

Visual Representation:

To visualize this circle, imagine plotting the center point (5, 6) on a coordinate plane. From this point, you would draw a circle with a radius of 9 units extending in all directions.

Key Points to Remember:

  • The equation (x-5)^2 + (y-6)^2 = 81 represents a circle.
  • The center of the circle is (5, 6).
  • The radius of the circle is 9 units.

By understanding the standard form and the components of the equation, we can easily identify the properties of the circle and visualize its shape.

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