Question

Write the standard equation of a circle with center (−1, −1) and radius 1.

Answer 1

Formula for circle:
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) is the cry and r is the radius.
(x - - 1)^2 + (y - - 1)^2 = 1^2
(x + 1)^2 + (y + 1)^2 = 1

Answer 2

The standard equation is
`(x+1)^2+(y+1)^2=1`

Explanation:

In order to determine the standard equation of a circle, we have to know the formula and its graph.

The standard form equation of a circle is a way to express the definition of a circle on the coordinate plane.

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

Where:

`(h,k)` are the "x" and "y" coordinates of the center of the circle respectively.

"r" is the radius of the circle.

I have attached an image that shows the graph of a circle.

In this case:

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

Finally, the standard equation of a circle with center (-1,-1) and radius 1 is

`(x+1)^2+(y+1)^2=1`