Fill in the blank(s) to correctly complete each sentence. The circle with equation x^2+y^2=49 has center with coordinates________ and radius equal to__________ .

Key Concepts

Equation of a Circle

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) represents 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), as there are no h or k values subtracted from x or y in the standard form.

Radius of a Circle

The radius of a circle is the distance from the center to any point on the circle. It can be found by taking the square root of the value on the right side of the equation when in standard form. Here, since 49 = r², the radius is r = √49 = 7.