completing the SQUARE: 4x^2 + 4y^2 - 16x + 40y + 36 = 0

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Math wiz ya rite 09

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Here's the question:

Complete the square to find the center and the radius of the circle:

4x^2+4y^2-16x+40y+36=0

I don't know where to begin. I havent seen a problem like this in class. Could someone please explain if they have time. Something basic on how you got to the answer would be great.

Thanks in advance,
DAnieL
 
Group your x's and y's first:

\(\displaystyle \L\\(4x^{2}-16x+?)+(4y^{2}+40y+?)=-36\)

Factor:

\(\displaystyle \L\\4(x^{2}-4x+?)+4(y^{2}+10y+?)=-36\)

Complete square in each, the square of half coefficient of x:

\(\displaystyle \L\\4(x^{2}-4x+4)+4(y^{2}+10y+25)=-36+16+100\)

Why 16 and 100 on the right?. Because of the 4 factored out. I had to multiply 4 and 25 by 4.

\(\displaystyle \L\\4(x-2)^{2}+4(y+5)^{2}=80\)

\(\displaystyle \L\\4[(x-2)^{2}+(y+5)^{2}]=80\)

\(\displaystyle \L\\(x-2)^{2}+(y+5)^{2}=20\)

The radius=\(\displaystyle sqrt{20}\)

Does that help?. Now you can tackle simlar problems
 
galactus said:
Group your x's and y's first:

\(\displaystyle \L\\(4x^{2}-16x+?)+(4y^{2}+40y+?)=-36\)

Factor:

\(\displaystyle \L\\4(x^{2}-4x+?)+4(y^{2}+10y+?)=-36\)

Complete square in each, the square of half coefficient of x:

\(\displaystyle \L\\4(x^{2}-4x+4)+4(y^{2}+10y+25)=-36+16+100\)

Why 16 and 100 on the right?. Because of the 4 factored out. I had to multiply 4 and 25 by 4.

\(\displaystyle \L\\4(x-2)^{2}+4(y+5)^{2}=80\)

Does that help?. Now you can tackle simlar problems
Click to expand...

is 80 the radius?
 
4x^2 + 4y^2 - 16x + 40y + 36 = 0

start by dividing every term by 4 to simplify ...

x^2 + y^2 - 4x + 10y + 9 = 0

group the x and y terms together ... move the constant

(x^2 - 4x) + (y^2 + 10y) = -9

complete the square for the x and y terms ...

(x^2 - 4x + 4) + (y^2 + 10y + 25) = -9 + 4 + 25

(x - 2)^2 + (y + 5)^2 = 20

standard form for a circle is ... (x - h)^2 + (y - k)^2 = r^2

now, answer the questions.
 
Look at what I gave you.

Everything.

\(\displaystyle x^{2}+y^{2}=r^{2}\)
 
stapel said:
What is the circle equation they gave you?
Click to expand...
Math wiz ya rite 09 said:
is 80 the 4x^2+4y^2-16x+40y+36=0
Click to expand...
Did they not cover circles and their equations in class or in the book...?

You should have been given something along the lines of "(x - h)<sup>2</sup> + (y - k)<sup>2</sup> = r<sup>2</sup>, where the center is at (h, k) and the radius is r". That's what you need to be working with.

Eliz.
 
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