question on standard form!!!

[mthcs]

Hi, I am given the equation x² + y² + -9x + -18y + 81 = 0 and am told to complete the square to find the standard form of the given equation. Then give the center and radius of the circle. Any help??? Thanks in advance!

 

[Deleted member 4993]

Hi, I am given the equation x² + y² + -9x + -18y + 81 = 0 and am told to complete the square to find the standard form of the given equation. Then give the center and radius of the circle. Any help??? Thanks in advance!

You are given a problem and the first step to the solution - how far did you progress with it?

If need help to review "completing the square" process, go to:

http://search.freefind.com/find.html?id=5014414&pageid=r&mode=ALL&n=0&query=completing+square

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[pka]

Hi, I am given the equation x² + y² + -9x + -18y + 81 = 0 and am told to complete the square to find the standard form of the given equation. Then give the center and radius of the circle. Any help??? Thanks in advance!

\(\displaystyle x^2-9x=\left(x^2-9x+\frac{81}{4}\right)-\frac{81}{4}\) is a completed square.

 

[mthcs]

I undestand that i am trying to get --> (x-h)^2 + (y-k)^2 = r^2 and I have determined that the radius is (9/2,9) but I cannot determine the standard form

 

[Mrspi]

I undestand that i am trying to get --> (x-h)^2 + (y-k)^2 = r^2 and I have determined that the radius is (9/2,9) but I cannot determine the standard form

What have you tried?

You were given this, right?

x² + y² + -9x + -18y + 81 = 0

Ok....group the terms containing x together, group the terms containing y together, and get that constant term OFF the left side by adding -81:

(x² - 9x + ......) + (y² - 18y + .....) + 81 + (-81) = 0 + (-81)

(x² - 9x + .....) + (y² - 18y + .....) = -81

Ok...complete the squares in the two trinomials in the parentheses....

for the first one, you need to divide -9 by 2, and square what you get. (-9/2)² is 81/4....add 81/4 to both sides:

(x² - 9x + 81/4) + (y² - 18y + ....) = -81 + (81/4)

And complete the square inside the second set of parentheses. Divide -18 by 2, square it, and add the result to both sides. -18/2 is -9, and (-9)² is 81:

(x² - 9x + 81/4) + (y² - 18y + 81) = -81 + (81/4) + 81

Ok...so we have this (having made each expression inside parentheses on the left side a perfect square):

[x - (9/2)]² + [y - 9]² = 81/4

Or,

[x - (9/2)]² + [y - 9]² = (9/2)²

Since this is now in the form

(x - h)² + (y - h)² = r², you should be able to see the center (h, k) and the radius r.

 

[mthcs]

thank you so much!!! i finally understand it!