find center and radius of circle with given equation:
(x+4)^2 + (y-4)^2 = 25
for (x-h)^2 + (y-k)^2 = r^2
the centre is (h,k) and the radius is r
so......
To find the center and radius of a circle with the equation (x+4)^2 + (y-4)^2 = 25, we can compare it with the standard equation for a circle:
(x-a)^2 + (y-b)^2 = r^2
where (a, b) represents the center and r represents the radius.
Comparing the given equation with the standard equation, we can see that:
- a = -4 (center's x-coordinate)
- b = 4 (center's y-coordinate)
- r^2 = 25 (radius squared)
Therefore, the center of the circle is (-4, 4) and the radius is 5.
To find the center and radius of a circle with a given equation, we need to write the equation in a specific form. The general equation of a circle is:
(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 equation is already in the correct form:
(x+4)^2 + (y-4)^2 = 25
Comparing this to the general equation, we can see that:
h = -4
k = 4
r^2 = 25
So, the center of the circle is (-4, 4), and the radius is the square root of 25, which is 5.