Find the standard equation of a circle with the center (0, 2) and a radius of 2 units.
To find the standard equation of a circle with the center (h, k) and a radius of r units, you can use the formula:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center is (0, 2) (where h = 0 and k = 2), and the radius is 2 units (r = 2).
Substituting these values into the formula, we get:
(x - 0)^2 + (y - 2)^2 = 2^2
x^2 + (y - 2)^2 = 4
Therefore, the standard equation of the circle with the center (0, 2) and a radius of 2 units is x^2 + (y - 2)^2 = 4.
(x-0)^2 + (y-2)^2 = 2^2
The standard equation of a circle is
(x-h)^2 + (y-k)^2 = r^2
Where h and k are the coordinates for the centre.
Hence(h, k) is (0, 2) respectively.
and the radius is 2 units
Now all you have to do is substitute it in.
(x-0)^2 + (y-2)^2 = 2^2
alas the standard equation is,
(x-2)^2 + (y-2)^2 = 4
Alas? All was good up till there.
The standard equation desired is indeed
x^2 + (y-2)^2 =4