Question

GEOMETRY)

Answer 1

Answer:

(x - 2)² + (y + 7)² = 64

(fourth option listed / option D)

Step-by-step explanation:

as you likely know, the equation of a circle (centered at origin) is x²+y²=r²

now, let's say we want to write this using the center (the origin), it could look like this:

(x - 0)² + (y - 0)² = r²

(the center is 0,0)

[we write this in parentheses when we are shifting the location of a point--similar to when we move a line on a graph]

We can use this for any center, and we write our circle equation as:

(x - h)² + (y - k)² = r²

(h, k) is the center

So, let's apply the information we know

our (h, k) is (2, -7)

so let's fill that in:

(x - h)² + (y - k)² = r²

(x - 2)² + (y - -7)² = r²          (simplify)

(x - 2)² + (y + 7)² = r²

now, we also know that our "r" (r is the radius) is 8, so let's fill that in too:

(x - 2)² + (y + 7)² = r²

(x - 2)² + (y + 7)² = 8²   (simplify)

(x - 2)² + (y + 7)² = 64

So, we have found the equation of our circle to be:

(x - 2)² + (y + 7)² = 64

hope this helps! (and hope this makes sense) have a lovely day :)