Question

Geometry Help Please!

Answer 1

hm, not quite, do you know how to complete the square?

Answer 2

ok, just look at the x part
(x^2 + 2x)
if you add 1, you get
x^2 + 2x + 1
which equals
(x+1)^2

do you understand where the 1 comes from?

Answer 3

I mean, do you understand why I added 1?

Answer 4

Nope, I didn't do anything to the 2x
I only added 1 so I could rewrite (x^2 + 2x) in the form (x+1)^2

Answer 5

(x^2 + 2x + 1) = (x+1)^2

Answer 6

(a+b)^2 = (a^2 + 2ab + b^2), have you seen this formula before?

Answer 7

Well, it's kinda hard to explain, but you want to rewrite (x^2 + 2x) in the form (a+b)^2 or (a-b)^2 by adding a number

Answer 8

can you try rewriting (y^2 + 4y + ___) in the form (y+b)^2? can you try filling in the blank so you get an expression in the form (y+b)^2

Answer 9

in other words, what value should we add to make the expression equal to (y+b)^2 where b is a constant?

i'm sorry, this is hard to explain D:

Answer 10

ok, I'll give you a hint:

we can add a number to
y^2 + 4y
to get
(y+2)^2

what is that number?

Answer 11

hint: try expanding (y+2)^2 = (y+2)(y+2)

Answer 12

what is (y+2)(y+2)?

Answer 13

yup! and how do we get from
y^2 + 4y
to
y^2 + 4y + 4?

Answer 14

this might be helpful in explaining the concept, http://www.purplemath.com/modules/sqrcircle.htm

Answer 15

nope, you add 4 to the expression

Answer 16

alright, I think I might have a better way to explain this...

Answer 17

ok, after all the math we just did, we have:

(x+1)^2 + (y+2)^2 = 20 + 4 + 1

remember, we added 4 and 1 to the left side, so we must add 4 and 1 to the right side

Answer 18

(x+1)^2 + (y+2)^2 = 25, are you with me so far?

Answer 19

alright, you know that the general equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where r is the radius and (h,k) is the center, right?

Answer 20

can you tell me what h, k, and r are, based on what we just found out?

Answer 21

not quite, check your math again
check the signs on h and k, and check r
r^2 = 25, so what is r?

Answer 22

right, and what are h and k?

Answer 23

not quite!

-h = 1
-k = 2

so, what are h and k?

Answer 24

yup! make sure to check the signs!

so, can you now tell me what the center and radius are?

Answer 25

yup, good job ~

Answer 26

that's it, look at the question again:

"find the center and the radius of the circle", so you're done

Answer 27

uh, sure

Answer 28

actually I need to go pretty soon, can I just outline my steps for you?
x^2 + 2x + y^2 + 4y = 20
(x^2+2x) + (y^2 + 4y) = 20
(x^2 + 2x + 1) + (y^2 +4y + 4) = 20 + 4 + 1 = 25
(x+1)^2 + (y+2)^2 = 25

h = -1
k = -2
r = 5

Answer 29

ok fantastic! you did perfectly, great job ~