X2+y2=16

The equation \( x^2 + y^2 = 16 \) represents a circle in the Cartesian coordinate system.

Key Characteristics of the Circle:

1. Center: The center of the circle is at the origin (0, 0).
2. Radius: The radius of the circle can be found by taking the square root of the constant on the right side of the equation. Here, the radius \( r \) is: \[ r = \sqrt{16} = 4 \]
3. Equation Form: This is the standard form of a circle's equation, which is given as \( (x - h)^2 + (y - k)^2 = r^2 \), where \( (h, k) \) is the center of the circle, and \( r \) is the radius.

Graphing the Circle:

To graph the circle, you can plot points that satisfy the equation \( x^2 + y^2 = 16 \). Some key points to plot include:

• \( (4, 0) \)
• \( (0, 4) \)
• \( (-4, 0) \)
• \( (0, -4) \)
• Points on the circumference found using other values of \( x \) or \( y \).

Additional Information:

• You can derive other important points by substituting values for \( x \) or \( y \) and solving for the other variable.
• The circle represents all points (x, y) that are exactly 4 units away from the center at the origin.

If you need help with specific problems or further analysis involving this equation, feel free to ask!