State the center and the radius of the circle represented by the equation
(x + 1)^2 + (y – 5)^2 = 64
If you tried to copy and paste, that does not work here.
State the center and the radius of the circle represented by the equation
(x + 1^2 + (y – 5)^2 = 64
I think the radius is 8 but am stuck on what the center represents here.
You mean (x+1)^2
Now this is the same both sides of x = -1
Like for x = -2 and for x = 0
in both cases (x+1)^2 = +1
In other words, x = -1 is an axis of symmetry and the circle center must lie on x = -1
Same thing for y = 5
so the center is at (-1,+5)
NOW
in general:
(x-h)^2 + (y-k)^2 = r^2
is circle with radius r
and center at (h,k)
I did get (-1,5) as well, but why is it -1 rather than 1? I was just wondering.
(x-h) = (x+1)
so
-h = +1
h = -1
To determine the center and radius of the circle represented by the equation (x + 1)^2 + (y - 5)^2 = 64, we can compare it to the standard form equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2.
In this equation, the values of h and k represent the coordinates of the center of the circle, and r represents the radius of the circle.
Comparing the given equation to the standard form equation, we can identify that the value of h is -1 and the value of k is 5. Therefore, the center of the circle is at (-1, 5).
To determine the radius of the circle, we can take the square root of the value on the right side of the equation. In this case, the square root of 64 is 8. Therefore, the radius of the circle is 8.
In conclusion, the center of the circle represented by the equation (x + 1)^2 + (y - 5)^2 = 64 is at (-1, 5), and the radius is 8.