Question

When baking cookies, each cookie should be placed about 2 inches from one another to allow room to expand. If one cookie has a radius of 1 inch and a center at C(1, –1), find the center and equation of the cookie immediately to the right. (Assume that each cookie is uniform with a radius of 1 inch and that 1 inch = 1 unit on a coordinate plane.)

Answer 1

Answer:

Center: (1, 3)

Equation: (x - 1)² + (y - 3)² = 1

Explanation:

1) The initial distance between the centers of two adjacent cookies must be equal to the separation indicated (2 inches) plus the radius of each cookie, which is 2 × 1 in.

So, the separation of the centers is 2 in + 2 × 1 in = 2in + 2 in = 4 in.

2) Then the coordinates of the center the cookie to the right of the given cookie are (1, -1 + 4) = (1, 3).

3) The equation of the circle of radius r and center (a,b) is:

(x - a)² + (y - b)² = r²

So, using a = 1, b = 3, and r = 1, you get:

(x - 1)² + (y - 3)² = 1