Question

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

x^2 −2x + y^2 − 6y = 26

Answer 1

do you know what a "perfect square trinomial" is?
often times just called a "perfect square"

Answer 2

Whenever facing an equation with the form:
\[x^2+y^2+Dx+Ey+F=0\]
we can calculate the center and the radius of the circle by the following equalities:
\[r=\sqrt{\frac{ D^2+E^2-4F }{ 4 }}\]
The center having coordinates \(C(\alpha, \beta)\), we can calculate alpha and beta by:
\[D=-2\alpha\]
\[E=- 2 \beta\]

Answer 3

I do, but I have never understood perfect square. @jdoe0001

Answer 4

well... have you done FOIL for expanding a squared binomial, like say \(\bf (x+3)^2?\)

Answer 5

No I haven't done FOIL, I don't even know what that is.

Answer 6

well... so hmm what section is this exercise covering?
what are you expected to use to get the circle's center and radius?

Answer 7

To get the center and the radius I have to use the equation that was provided.

Answer 8

yes...but how are you expected to find it from that equation?
I assume it's related to the convered material of say.. yesterday or last week

Answer 9

Hmm, I don't know. I guess I didn't take notes, but I remember that the equation can be graphed and that would make it easier to find the center and radius.

Answer 10

well... yes and no
you have two Y's for one, not just one
hmmm
do you know how to expand say \(\bf (2x+3)^2\)?

Answer 11

No I don't know how to expand that. I don't really know what that means.

Answer 12

I think you should read what Coffee said.

Answer 13

well... you'd want to cover factoring and expanding quadratics first then
including the perfect square trinomial, and also check your book on "completing the square" section

Answer 14

but since you haven't covered those.. then this exercise doesn't apply to you

Answer 15

Alright, I tried having my friend read what owl said to me but it made no sense.

Answer 16

unless, you'd want to use Owlcoffee 's suggestion, which I doubt you have covered either, or are intended to use anyway

Answer 17

What I have stated above are the formulas that will allow you to calculate both the radius and the center of the circle with only its equation.

Answer 18

@Keigh2015 I should say, even with my grade 11 knowledge of math, as a med student i could do what Coffee instructed to do. So just follow the formula he gave and you will get to your answer.

Answer 19

I am in 9th grade and I can't even begin to understand what Owl put, not meaning to sound rude or anything.

Answer 20

Keigh2015 the issue is, what I or Owlcoffee said, makes sense only in context

the issue is, you're correct, if you open a book and start reading at chapter 5, skipping 4 chapters, whatever chapter 5 is going to indicate, will have the same effect
no that there's anything wrong with chapter 5, so much that, you need to cover the material before it, that is, the other 4 chapters

so... just having someone explain you want the formula Owlcoffee posted does or say
won't help you understand the material

Answer 21

So, I would have to read my book to be able to correctly get this answer?

Answer 22

x2+y2+Dx+Ey+F=0

now when you look at your equation its:

x^2 −2x + y^2 − 6y = 26
x and y are as they are, D is the number that comes with x which is 2 in your case, E is the number that comes with y which is 6 in your case, F is 26 in your case that is moved to the other side of equation.
He wants you to arrange your equation the way he gave there, but make sure you are putting YOUR correct signs when you are moving the values to formulate your equation the way he wrote, which means it doesnt necessarily have to be '+' there but also can be negative

we can calculate the center and the radius of the circle by the following equalities:
now just use the other formula he gave and replace D with the number before x, dont forget the sign of it, same with D and F
then calculate

The center having coordinates C(α,β), we can calculate alpha and beta by:
D=−2α
you have the value for D with its sign and alpha is like x so just solve it
E=−2β
same thing here.

Answer 23

Wow, ok, that was a lot to listen to.