Question

What is the radius of a circle with the equation

Answer 1

\[x ^{2}+y ^{2}+4x+8y-10=0\]

Answer 2

Complete the square.

Answer 3

any idea how to complete the square? your goal is to make this look like
\[(x-h)^2+(y-k)^2=r^2\] the circle with center \((h,k)\) and radius \(r\)

Answer 4

I ended up with (x-2)^2+(y-3)^2=23/x but I feel like I did one step incorrectly.

Answer 5

so you have to complete the square twice in order to turn \[x ^{2}+y ^{2}+4x+8y-10=0\] in to something that looks like \[(x-h)^2+(y-k)^2=r^2\]

Answer 6

both minus signs in your answer are a mistake, there is no minus sign in our question

Answer 7

lets go slow

Answer 8

\[x ^{2}+y ^{2}+4x+8y-10=0\] group the terms together to get
\[x^2+4x+y^2+8y=10\]

Answer 9

then it is not too bad
for the \(x\) part half of \(4\) is \(2\) and \(2^2=4\) so the first part becomes
\[(x+2)^2+y^2+8y=10+4=14\]

Answer 10

Ah I see, I followed an example similar, then I guess I messed up.

Answer 11

repeat the process for the \(y\) terms
half of \(8\) is \(4\) and \(4^2=16\) so write as
\[(x+2)^2+(y+4)^2=14+16=30\]

Answer 12

now read off the answer directly
\((h,k)\) is \((-2,-4)\) your center and \(r^2=30\) so the radius is \(\sqrt{30}\)

Answer 13

Ah cool I ended up doing the problem correctly the second time.Thank you so much!

Answer 14

yw