Write the equation of a circle with a center at (15, –35) and a diameter of 100.
To write the equation of a circle with a center at (15, -35) and a diameter of 100, we need to use the standard form of the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) represents the coordinates of the center and r represents the radius of the circle.
Given that the center is (15, -35), we substitute h = 15 and k = -35 into the equation:
(x - 15)^2 + (y - (-35))^2 = r^2
Since the diameter is 100 and the radius is half the diameter, we have r = 100/2 = 50.
Now we can rewrite the equation of the circle with the given values:
(x - 15)^2 + (y + 35)^2 = 50^2
Simplifying further, we have:
(x - 15)^2 + (y + 35)^2 = 2500
Therefore, the equation of the circle with a center at (15, -35) and a diameter of 100 is (x - 15)^2 + (y + 35)^2 = 2500.
To write the equation of a circle, we need to know the coordinates of its center and its radius. Since the diameter is given as 100, we can find the radius by dividing the diameter by 2.
The center of the circle is given as (15, -35), which means that the x-coordinate of the center is 15 and the y-coordinate is -35.
Let's start by finding the radius:
Radius = Diameter / 2
Radius = 100 / 2
Radius = 50
Now, we can write the equation of the circle using the formula:
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) is the center of the circle, and r is the radius.
Substituting the values we have:
(x - 15)^2 + (y - (-35))^2 = 50^2
Simplifying further:
(x - 15)^2 + (y + 35)^2 = 2500
So, the equation of the circle is (x - 15)^2 + (y + 35)^2 = 2500.