Question

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Answer 1

Circle B:

`(x+4)^2+(y+3)^2=4`

Circle F:

`(x-4)^2+(y-1)^2=16`

Explanation:

We can write the equation of a circle equation with center on (h,k) and radius r as:

`(x-h)^2+(y-k)^2=r^2`

Then, we analyze the circle will have for the circle B:

- It has a center in x=-4 and y=-3.

- It radius can be calculated from the distance from the center (x,y)=(-4,-3) to one of its points (x,y)=(-4, -1). Then, its radius is r=2.

Then, we can write the equation as:

`(x-h)^2+(y-k)^2=r^2\\\\h=-4\\k=-3\\r=2\\\\(x+4)^2+(y+3)^2=4`

we analyze the circle will have for the circle F:

- It has a center in x=4 and y=1.

- It radius can be calculated from the distance from the center (x,y)=(4, 1) to one of its points (x,y)=(0, 1). Then, its radius is r=4.

Then, we can write the equation as:

`(x-h)^2+(y-k)^2=r^2\\\\h=4\\k=1\\r=4\\\\(x-4)^2+(y-1)^2=16`