Question

WILL FAN AND MEDAL FOR EXPLAINATION
Using the following equation, find the center and radius of the circle.
x^2 + 2x + y^2 + 4y = 20

Answer 1

do u have any idea

Answer 2

Caution: Please use the symbol ^ to express exponentiation:

x2 + 2x + y2 + 4y = 20 NO

x^2 + 2x + y^2 + 4y = 20 YES


The standard equation of a circle centered at the point (h,k) and with radius r is:\[(x-h)^2+(y-k)^2=r^2\]

Answer 3

\[(x-h)^{2}+ (y - k)^{2}= r ^{2}\]
is the standard form of circle equation whose center = (h ,k) and radius =r

Answer 4

So, to rewrite x^2 + 2x + y^2 + 4y = 20 in the proper form (standard equation of a circle), you're going to have to "complete the square" twice in x^2 + 2x + y^2 + 4y = 20. Are you familiar with "completing the square?"

Answer 5

I have no idea what completeing the square means

Answer 6

Let's look at the first two terms of x^2 + 2x + y^2 + 4y = 20.

We want to re-write x^2 + 2x as the "perfect square" of a binomial.

Right off, I'll share the correct end result: x^2 + 2x + 1 - 1.
Please note that the first 3 terms are the "perfect square) of (x+1)."

How to do this?

Starting with x^2 + 2x,
1) Take ONE HALF of the coefficient of x. That's 2, so ONE HALF of that coeff. is 1.
2) Add 1, and then subtract 1, from x^2+2x.

Result: x^2 + 2x + 1 - 1 = (x+1)^2 - 1

Any questions about this procedure?

Answer 7

[x^2 +2*x*1 + 1^2]+[y^2 + 2 *y *2 +2^2] = 15

we are making the equation into (a+b) ^2 form

Answer 8

(x+1)^2 + (y +2)^2 =sqrt 15

Answer 9

\[(x+1)^{2}+ (y+2)^{2}= (\sqrt{15})^{2}\]

Answer 10

ok so why would you take Take ONE HALF of the coefficient of x. and then I understand from there

Answer 11

\[a ^{2} + 2\times a \times b +b ^{2} = (a+b)^{2}\]compare

\[x ^{2} + 2 \times x \times 1 + 1^{2} - 1^{2}\]

Answer 12

do u understand

Answer 13

Not really where did these numbers come from

Answer 14

"completing the square" is a commonly used method of algebra used for solving quadratic equations, locating the centers and radii of circles, and so on.
Have you not found any mention of "completing the square" in your online learning materials or in your textbook?

Answer 15

x^2 +2x +y^2 +4y + 5 = 15 can i write ur equation like this

Answer 16

Let me ask the same questions then, in connection with your geometry course.
Have you come across any example problems in which someone explains how to find the center and radius of a circle from a given equation such as x^2 + 2x + y^2 + 4y = 20 ?

Aren't there any examples in your textbook or online learning materials?

Answer 17

I think, let me find it real quick

Answer 18

http://www.regentsprep.org/regents/math/algtrig/atc1/circlelesson.htm

Answer 19

http://paec.flvs.net/educator/student/frame_toolbar.cgi?chenderson146*kyah*mpos=1&spos=0&option=hidemenu&slt=uSfGEEEIW9sQc*4080*http://paec.flvs.net/webdav/educator_geometry_v16/index.htm

Answer 20

Let's look at the "y-terms" of the given equation x^2 + 2x + y^2 + 4y = 20.

First, let's go thru the procedure of completing the square applied to y^2 + 4y.

Look at the coefficient of y here; it is 4.
Take half of that: result is 2
Square this last result: next result is 4

Now add 4 and then subtract 4 from y^2+4y.

Result: y^2+4y + 4 - 4.

Note that y^2+4y+4 is a "perfect square," equal to (y+2)^2.

Thus, your final result would be (y+2)^2-4.

You need to understand the various steps of this procedure. With a little practice, the procedure becomes almost automatic, easy to do.

Can you go back to x^2 + 2x and complete the square, following the same steps shown immediately above?

Answer 21

I see you've tried to share something from FLVS, but since I don't have the password, I can't access it. Sorry. Either find another way to share this info (as thru sharing a screen shot), or let's go thru my examples again. Your choice.

Answer 22

Let's go thru this problem again, with your participation:

Given: x^2 + 2x + y^2 + 4y = 20

Let's "complete the square" for x^2 + 2x.

What is the coefficient of "x" in x^2 + 2x?

(Awaiting your answer)

Answer 23

The coefficient of x i think would be 2, then I half it and get 1 and 1 squared= 1
After that I dont understand the " Now add 4 and then subtract 4 from y^2+4y." from your example

Answer 24

Your given equation has two parts on the left side: x terms and y terms.

You are correct: x^2 + 2x becomes x^2 + 2x + 1 - 1, or (x+1)^2 -1.

Use exactly the same steps to rewrite y^2 + 4y. Awaiting your answer.

Answer 25

ok so the coefficint of y would be 4. I would then half it, getting 2, then i square that and get 4,so (y+2)^2-4, which for both of them put together would be (x+1)^2 -1+ (y+2)^2-4= 20

Answer 26

yup, now put the -1 and the -4 on the other side and you should recognise that the equation is the normal form of the equation for a circle.

Answer 27

So, please add 1+4 (or 5) to both sides of your latest equation. This will remove the -4 and the -1 from the left side.

What do you get? You'll most likely have the desired equation of this circle in standard form. What's 20 + 1 + 4? If that's a perfect square, find the square root (r) and rewrite the right side as r^2.