Question

I need HELP ASAP!! Please explain how to solve the problem

Answer 1

`(x+1)^2+(y+4)^2=9\\`

Explanation:

The general format for the equation of a circle is the following:

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

Where
`(h,k)` is the center of the circle and (
`a`) is the circle's radius. Please note, that the circle (
`(x-h)^2+(y-k)^2=a^2\\`) has a center that is (h) units to the right of the origin, and (k) units above the origin.

The given circle has a center at
`(-1,-4)`, moreover, its radius is (3) units. Therefore, one must substitute these points into the equation of a circle and simplify to find its equation:

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

`(x-(-1))^2+(y-(-4))^2=(3)^2\\`

`(x+1)^2+(y+4)^2=9\\`

Answer 2

Step-by-step explanation: Let's first determine the center of the circle

which is represented by the red dot and it has the coordinates (-1, -4).

The radius of the circle is a segment that joins the center of the

circle to a point on the circle and all radii of a circle are congruent.

The radius of the circle shown here is 3.

Now, the equation of a circle is (x - h)² + (y - k)² = r² where

(h, k) is the center of the circle and r is the radius.

Now we plug all our given information into the formula.

So we have [x - (-1)]² + [y - (-4)]² = (3)².

Notice that I changed the parentheses in the formula to brackets

so that we wouldn't be dealing with too many sets of parentheses.

Changing the brackets back to parentheses,

our equation is (x + 1)² + (y + 4)² = 9.