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

As per the problem,

When baking cookies, each cookie should be placed about 2 inches from one another to allow room to expand.

Also

One cookie has a radius of 1 inch and a center at C(1, –1).

We are supposed to find the center and equation of the cookie immediately to the right.

First we will draw the circle to see its actual position and then we will find the center of the circle(Cookies) on immediate right

The cookies has a gap of 2 inches and radius of 1 inch. So the x-coordinate of the cookie(Circle) on immediate right will be $2+2+1=5$

There will be no change change in the y-coordinate of the center of the circle (Cookie) because both the cookies are lying in the same line.

Hence the center of the circle (Cookie) on immediate right of the given cookie is (5,-1), and radius will be 1.

Hence the equation can be found by substituting the values in the standard form of circle

$(x-h)^2+(y-k)^2=r^2\\ \\ \text{where (h,k) is center and r is the radius of the circle.}\\ \text{Now substitute the values we get}$

$(x-5)^2+(y+1)^2=1^2\\ \\ \Rightarrow (x-5)^2+(y+1)^2=1$