Using the following equation, find the center and radius: x2 + 2x + y2 + 4y = 20 The center is located at (1, 2), and the radius is 25. The center is located at (-1, 2), and the radius is 25. The center is located at (-1, -2), and the radius is 5. The center is located at (1, 2), and the radius is 5.

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Using the following equation, find the center and radius: x2 + 2x + y2 + 4y = 20 The center is located at (1, 2), and the radius is 25. The center is located at (-1, 2), and the radius is 25. The center is located at (-1, -2), and the radius is 5. The center is located at (1, 2), and the radius is 5.

Mathematics
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HI!!
this is a job for "completing the square" you have to do it twice, once for \(x^2+2x\) and again for \(y^2+4y\) it is not too hard do you know how to do it?

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Other answers:

no
ok lets start with \[x^2+2x\] what is half of 2?
1
right and now what is \(1^2\_?
1
oops what is \(1^2\)?
ok so we turn \[x^2+2x\] in to \[(x+1)^2\] and add 1 to the other side making it \[(x+1)^2+y^2+4y=21\]
now repeat with \(y^2+4y\) what is half of 4?
2
ok and \(2^2\)?
2
hmm no
sorry 4
right so turn \(y^2+4y\) in to \((y+2)^2\) and add 4 to the other side
now we are at \[(x+1)^2+(y+2)^2=25\] and from that you can read off the center and the radius as it is in standard form for a circle
you good from there?
Yea so the answer is (-1,-2) radius 5?
yes
thx
\[\color\magenta\heartsuit\]
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