Re: Complete the equation?

Quote:

Originally Posted by

**M670**

YES and $\displaystyle r^2=(-7-4)^2+(9-1)^2$

You should know the basic algebra: $\displaystyle (x+7)^2=x^2+14x+49$.

Re: Complete the equation?

Hello, M670!

Quote:

$\displaystyle \text{Find the equation of the circle centered at }C(\text{-}7,9)\text{ that passes through }P(4,1).$

You're making hard work out of it . . .

The equation of a circle with center $\displaystyle (h,k)$ and radius $\displaystyle r$ is: .$\displaystyle (x-h)^2 + (y-k)^2 \:=\:r^2$

You already know the center: .$\displaystyle C(\text{-}7,9)$

You need only the radius . . . $\displaystyle r \:=\:\overline{CP}$

. . Use the Distance Formula.

Re: Complete the equation?

Quote:

Originally Posted by

**Plato** YES and $\displaystyle r^2=(-7-4)^2+(9-1)^2$

You should know the basic algebra: $\displaystyle (x+7)^2=x^2+14x+49$.

So I came up with $\displaystyle x^2+14x+y^2-18y+130=0$ but that still isn't right and I dont know why? I need to write formula =0

Re: Complete the equation?

Quote:

Originally Posted by

**M670** So I came up with $\displaystyle x^2+14x+y^2-18y+130=0$ but that still isn't right and I dont know why? I need to write formula =0

You did not use the fact $\displaystyle r^2=185$, did you?

Re: Complete the equation?

Quote:

Originally Posted by

**Plato** You did not use the fact $\displaystyle r^2=185$, did you?

No I did not use the $\displaystyle r^2=185$ as I know the circle formula to be [tex](x-h)^2+(y-K)^2=r^2[/tex} since it's asking me for the equation equal to zero I am not sure where I would put radius?

Re: Complete the equation?

Quote:

Originally Posted by

**M670** No I did not use the $\displaystyle r^2=185$ as I know the circle formula to be [tex](x-h)^2+(y-K)^2=r^2[/tex} since it's asking me for the equation equal to zero I am not sure where I would put radius?

I don't think any of us can help you understand this question.

Your misunderstanding is very profound.

Please sit down with a live tutor. Go over what this question means.

Re: Complete the equation?

Quote:

Originally Posted by

**Plato** I don't think any of us can help you understand this question.

Your misunderstanding is very profound.

Please sit down with a live tutor. Go over what this question means.

Thanks for trying, Its this web program called webworks, It really sucks as you have to answer it a specific way or esle it wont except it.

Re: Complete the equation?

You know that the centre is $\displaystyle \displaystyle \begin{align*} (-7, 9) \end{align*}$ and one point on your circle is $\displaystyle \displaystyle \begin{align*} (4, 1) \end{align*}$. The radius is the distance between the centre to any point on the circle, so how can you work out the distance between these two points?

Re: Complete the equation?

Quote:

Originally Posted by

**Prove It** You know that the centre is $\displaystyle \displaystyle \begin{align*} (-7, 9) \end{align*}$ and one point on your circle is $\displaystyle \displaystyle \begin{align*} (4, 1) \end{align*}$. The radius is the distance between the centre to any point on the circle, so how can you work out the distance between these two points?

Yes I know I can use the standard distance formula which will give my radius of the circle but the question was asking me the equation of a circle with its center at (-7,9) and passes throught points (4,1)

Re: Complete the equation?

Quote:

Originally Posted by

**M670** Yes I know I can use the standard distance formula which will give my radius of the circle but the question was asking me the equation of a circle with its center at (-7,9) and passes throught points (4,1)

Well damn it, use it!

Re: Complete the equation?

I don't think you've bothered reading the posts above you. If you have the centre and radius of your circle, substitute them into this:

$\displaystyle \displaystyle \begin{align*} (x - h)^2 + (y -k)^2 = r^2 \end{align*}$

where $\displaystyle \displaystyle \begin{align*} (h, k) \end{align*}$ is the centre of your circle and $\displaystyle \displaystyle \begin{align*} r \end{align*}$ is the radius.

This is the general form of the equation of a circle. But since you are asked to set the equation equal to 0, you expand everything and move everything to one side.

Re: Complete the equation?

Ok So $\displaystyle h=-7 k=9 r= \sqrt185$ $\displaystyle (x+7)^2+(y-9)^2=\sqrt185$ which is then $\displaystyle x^2+14x+49+y^2-18y+81=\sqrt185 $

HOLY SH** it just dawned on me $\displaystyle x^2+14x+y^2-18y-55=0$ is the correct answer....

Let's hope it doesn't take me this long on my final...

Many thanks Prove it and Plato...

Re: Complete the equation?

Actually $\displaystyle \displaystyle \begin{align*} r = \sqrt{185} \end{align*}$ so $\displaystyle \displaystyle \begin{align*} r^2 = 185 \end{align*}$ which means $\displaystyle \displaystyle \begin{align*} (x + 7)^2 + (y - 9)^2 = 185 \end{align*}$.