the center of a circle
x^2 + y^2 + 8y =1 is
a. (0,-2)
b. (0,4)
c. (0,1)
d. (0,-4)
I believe the answer is (0,4)
Am I correct ?
Incorrect!
you have to complete the square to get it into standard form
x^2 + y^2 + 8y + 16 = 1 + 16
x^2 + (y+4)^2 = 17
Now what do you know from your previous posts on this?
I'm not sure what your looking for Reiny. It looks like the center of the circle is still (0,4) what am I doing wrong?
(x+0)^2 + (y+4)^2 = 17
the center would be (0,4)
I can't see it any other way ...arghhhh
I pointed out the pattern for you in
http://www.jiskha.com/display.cgi?id=1325732520
and you seem to be able to understand in your posts that follow it,
Now suddenly you have it backwards again.
remember that the sign is opposite what you see in the brackets
so for (x-5)^2 + (y+7)^2 = 100
the centre would be (+5, -7)
so for the above question is would obviously be
(0, -4)
ARGHHHHH now that really was a brain fart on my part ...
Thanks a lot Reiny for the help
Don
To find the center of a circle given its equation, you need to rewrite the equation in the standard form, which is (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.
Let's rewrite the given equation: x^2 + y^2 + 8y = 1.
First, complete the square for the y-terms:
x^2 + y^2 + 8y = 1
x^2 + (y^2 + 8y + 16) = 1 + 16
x^2 + (y + 4)^2 = 17
Now, since the equation is in standard form, we can see that the center of the circle is at (0, -4), and the radius is the square root of 17.
According to your options, the correct answer is not (0, 4), but rather (0, -4).
So, (d) is the correct answer.