Question

What is the standard form of the equation of the circle in the graph

Answer 1

The standard form of a circle:

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

`(h;\ k)` - the coordinates of a center of a circle

`r` - the radius

We have:

the center:
`(0;\ -4)`

the radius:
`r=2`

substitute

`(x-0)^2+(y-(-4))^2=2^2\\\\x^2+(y+4)^2=4`

Answer 2

When an equation of circle is expressed in the form:

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

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

The center = the coordinate you have plotted on the graph.

Radius = how many units long the circle extends to.

SO, let's plug this in.

Coordinate plotted = (0, -4)

0 = h

-4 = k

(x - {0})^2 + (y - {-4})^2 = 2^2

(x - 0)^2 + (y + 4)^2 = 4

(whenever we have two negative signs next to each other, it turns the digit to the right of the final negative sign positive.)

Now we are left with this final equation as a solution:

x^2 + (y + 4)^2 = 4.

I hope this helped~!