Question

Using the following equation, find the center and radius of the circle.

x2 + 2x + y2 + 4y = 20

Answer 1

@mathmate

Answer 2

You would complete the squares (of x and y).

Answer 3

Separating them into two equations?

Answer 4

Trying it again without the typos :)

If you look at the x^2 + 2x and the y^2 + 4y, you can "complete the square". For example, x^2 + 2x are the first two terms of the perfect "square" x^2 + 2x + 1 or (x + 1)^2 and y^2 + 4y are the first two terms of the perfect "square" y^2 + 4y + 4 or (y + 2)^2

Answer 5

\[x^2+2x+y^2+4y=20\]
\[(x+1)^2+(y+2)^2=20+1+4\]
I'll let you finish the problem.

Answer 6

Yes :)

Answer 7

Yes, kind of, but they remain in the same equation (of the circle)

Answer 8

Okay, let me finish the problem real quick! @anteater @mathmate

Answer 9

Wait, but do I do anything to this? --> (x+1)2+(y+2)2
the other part equals to 25

Answer 10

Do I distribute it, is what I mean.

Answer 11

In a standard circle centred at h,k with radius r, the equation is
\[(x-a)^2+(y-b)^2=r^2\]
I'm sure you can figure out the centre and radius of the given circle.

Answer 12

OH, now that actually helps. Thanks..I;m sure I can figure it out too.

Answer 13

Sorry, the standard circle I gave had centre (a,b), and not (h,k) as I said.
It was a typo. :(

Answer 14

It's all good, :) It took me a good 2 minutes to figure that out haha :) Thanks! @mathmate and thanks @anteater

Answer 15

Welcome :) I figured I should just step aside since you guys were working away on it. :D

Answer 16

Haha yeah thank you for that! I usually get confused when there's more than one person explaining at the same time..so sensible of you :))

Answer 17

Anteaters are known for sensibility. ;)

Answer 18

But of course both of you helped in your own ways! (:

Answer 19

Sometimes.

Answer 20

LOl haha ;))

Answer 21

Do you have any problems that involve ellipses or hyperbolas?

Answer 22

It's been a pleasure. Catch up with you guys later!

Answer 23

Ok :)

Answer 24

@anteater Nope! @mathmate ok :)

Answer 25

Ok :) I hope you have a great afternoon! :D

Answer 26

Thanks, you too!