The outside edge of a circular saw whose dimensions are measured in inches can be defined by the equation x2 + y2 = 33.0625. A hole needs to be cut in the center that can be defined by the equation x2 + y2 = 3.0625. The centers of the two curves are----------------- . The difference in the diameters of the circles is--------------------------- inches.

A circle can be characterized by its center's location and its radius's length. The centres of the two curves are at origin (0,0). The difference in the diameters of the circles is 8 inches.

What is an equation of a circle?

A circle can be characterized by its center's location and its radius's length.

Let the centre of the considered circle be at (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x-h)² + (y-k)² = r²

The centre of the two circles lies at the origin(0,0), therefore, at the same place.

The equation of the outside edge of a circular saw is,

x² + y² = 33.0625

x² + y² = (5.75)²

Therefore, the radius of the outside edge of a circular saw is 5.75 inches. Thus, the diameter of the outside edge of a circular saw is 11.5 units.

The equation of the hole is,

x² + y² = 3.0625

x² + y² = (1.75)²

Therefore, the radius of the outside edge of a circular saw is 1.75 inches. Thus, the diameter of the hole is 3.5 inches.

Now, the difference in the diameters of the circles is,

Difference = 11.5 inches - 3.5 inches = 8 inches

Hence, The centres of the two curves are at origin (0,0). The difference in the diameters of the circles is 8 inches.

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