Determine the center and the radius of the following circle:
x^2+y^2+8x-2y=8
so I figured I'd use completing the square after putting it in standard form:
(x^2+8x)+(y^2-2y)=8
I'm not sure where to go from here.
but you didn't "complete" the square
(x^2+8x)+(y^2-2y)=8
(x^2+8x + 16)+(y^2-2y + 1)= 8 + 16 + 1
(x+4)^2 + (y-1)^2 = 25
Now we have it in standard form.
Can you take it from there ?
Ok. Do I take the square root of the whole thing now?
getting x+4-y-1+-sqrt25
x-y=3+-sqrt25
I've never done this before, I'm not sure if this is even right and if it is, I definitely don't know where to go from here
no,
the standard equation of a circle with centre (h,k) and radius r is
(x-h)^2 + (y-k)^2 = r^2
so we ended up with
(x+4)^2 + (y-1)^2 = 25 or
(x+4)^2 + (y-1)^2 = 5^2
then the centre is (-4,1) and radius is 5
Here is an interesting page for your topic
http://www.analyzemath.com/CircleEq/Tutorials.html
Thanks so much for your explanation. I was able to figure it out and now got your answer.
To determine the center and radius of the circle, you're on the right track by completing the square. Let's continue with that process.
First, let's rearrange the equation to group the "x" terms and the "y" terms separately:
(x^2 + 8x) + (y^2 - 2y) = 8
To complete the square for the "x" terms, we need to add a specific value inside the parentheses. To figure out what that value is, take half of the coefficient of the "x" term (which is 8), square it, and add it inside the parentheses:
(x^2 + 8x + 16) + (y^2 - 2y) = 8 + 16
Notice that we added 16 inside the first parentheses. Now, let's do the same for the "y" terms:
(x^2 + 8x + 16) + (y^2 - 2y + 1) = 8 + 16 + 1
Here, we added 1 inside the second parentheses. Now we have a perfect square for both "x" and "y" terms. Let's rewrite the equation:
(x + 4)^2 + (y - 1)^2 = 25
Now, the equation is in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2. We can identify the center and radius of the circle by comparing the equation to this standard form.
The center of the circle is the opposite of the values inside the parentheses, so the center is (-4, 1).
The radius of the circle is the square root of the value on the right side of the equation, which is 25. Thus, the radius is √25, which simplifies to 5.
Therefore, the center of the circle is (-4, 1), and the radius is 5.