Question

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.

x2 − 4x + y2 + 8y = −4

Answer 1

suppose i don't want to show all my work? can i get partial credit?

Answer 2

I don't want the answer. I want you to help me do it

Answer 3

the idea is to complete the square twice, once for
\[x^2-4x\] and again for \[y^2+8y\]

Answer 4

4x^2 and 8y^2

Answer 5

oh no

Answer 6

have you learned how to "complete the square"?

Answer 7

no

Answer 8

then you can't do this problem

Answer 9

oh

Answer 10

i will show you how to complete the square for \(x^2-4x\)
what is half of 4?

Answer 11

2

Answer 12

right so we start with
\[x^2-4x+y^2+8x=-4\]and turn it in to
\[(x-2)^2+y^2+8y=-4+2^2\]

Answer 13

or\[(x-2)^2+y^2+8y=0\] now we repeat with \(y^2+8y\)

Answer 14

what is half of 8?

Answer 15

4

Answer 16

so we go right to
\[(x-2)^2+(y+4)^2=0+4^2\]

Answer 17

or just
\[(x-2)^2+(y+4)^2=16\] now your circle is in standard form and you can read off the center and radius from the equation

Answer 18

ok thank you

Answer 19

yw

Answer 20

I'm so sorry. when I look at numbers, they get mixed up in my head and I don't understand math in the first place.