CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The circle with equation x² + y² = 49 has center with coordinates ________ and radius equal to _______.

Key Concepts

Circle Equation

The standard equation of a circle in a Cartesian coordinate system is given by (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. In this case, the equation x² + y² = 49 can be rewritten to identify the center and radius directly.

Center of a Circle

The center of a circle is the point from which all points on the circle are equidistant. For the equation x² + y² = 49, the center is at the origin (0, 0) because there are no h or k values subtracted from x or y, indicating that the circle is centered at the coordinate axes.

Radius of a Circle

The radius of a circle is the distance from the center to any point on the circle. In the equation x² + y² = 49, the radius can be found by taking the square root of 49, which equals 7. Thus, the radius is 7 units.