write the equation in standard form for the circle with center (0,5) and radius 1
Hey, look, all you really need is the first line
(x-h)^2 + (y-k)^2 = r^2
That's correct! The general equation of a circle with center (h,k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
This form of the equation is called the standard form of the equation of a circle.
To write the equation in standard form for the circle with center (0, 5) and radius 1, we can use the formula for a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) represents the center of the circle and r represents the radius.
In this case, the center is (0, 5) and the radius is 1. Substituting these values into the formula, we get:
(x - 0)^2 + (y - 5)^2 = 1^2
Simplifying further, we have:
x^2 + (y - 5)^2 = 1
Therefore, the equation in standard form for the circle with center (0, 5) and radius 1 is:
x^2 + (y - 5)^2 = 1
The equation for a circle with center (h,k) and radius r is:
(x-h)^2 + (y-k)^2 = r^2
Substituting the given values, we get:
(x-0)^2 + (y-5)^2 = 1^2
Simplifying and expanding, we get:
x^2 + y^2 - 10y + 25 = 1
x^2 + y^2 - 10y + 24 = 0
Therefore, the equation in standard form for the circle with center (0,5) and radius 1 is:
x^2 + y^2 - 10y + 24 = 0.