Show that the equation represents a circle by rewriting it in standard form, and find the center and radius of the circle.
x2 + y2 + 4y + 2 = 0

- anonymous

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- anonymous

- anonymous

can u helpme

- saifoo.khan

@Directrix are you good with circles?

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## More answers

- anonymous

noup

- anonymous

help mee

- anonymous

sir

- anonymous

helloo

- Directrix

@Shaks
I'm hoping you understand the process of completing the square. We'll need that to get x2 + y2 + 4y + 2 = 0 into the standard form of the equation of a circle.
That standard form is (x - h) ^2 + (y - k) ^2 = r^2 where (h,k) are the coordinates of the center of the circle and r is the radius of the circle. Check out the attachment.

##### 1 Attachment

- anonymous

is that the asnwer

- Directrix

No. Focus on the process, not the answer.

- anonymous

yeaa

- anonymous

getting it kind it

- anonymous

of

- anonymous

The center is (0,-2)

- Directrix

So, x^2 + y^2 + 4y + 2 = 0 can be written as x^2 + y^2 + 4y + __4_ = 0 + 4
(x + 0) ^2 + (y + 2) ^2 = 4 ---> Your Circle
Now, look at the standard form for the circle equation, compare it to the equation, and pick out the coordinates of the center and the value of the radius.
Post what you get, and I'll check. @Shaks

- Directrix

r = ?

- anonymous

x^2+(y+2)^2=3 is this the standerd form

- anonymous

r= -2

- anonymous

hello

- anonymous

are u there

- Directrix

r= -2 --> Incorrect

- anonymous

then how to solve it

- Directrix

Look at standard form for circle equation:
That standard form is (x - h) ^2 + (y - k) ^2 = r^2 where (h,k) are the coordinates of the center of the circle and r is the radius of the circle.
What positive number times itself = 4? That's your r.

- anonymous

2 is r

- Directrix

Correct.

- anonymous

got it

- anonymous

noo r is not 2

- anonymous

is it 4

- Directrix

@Shaks I messed up by dropping the 2.
So, x^2 + y^2 + 4y + 2 = 0 can be written as x^2 + y^2 + 4y + __4_ = 2 + 4 = 6.
r^2 = 6 and r is square root of 6.

- anonymous

is it 6

- anonymous

2.44

- Directrix

6 = r^2. We want r which is square root of 3.

- anonymous

hmm

- anonymous

trying to understand

- anonymous

1.7

- anonymous

did not get it it too doficult

- anonymous

difficult

- Directrix

You approximated square root of 3 to get 1.7.
I stick with exact form but I don't know what your options are.

- anonymous

yaa i got it

- anonymous

Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)
x + 42
= x

- anonymous

now 1 more sum

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