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#1 2006-12-10 16:57:00

Jedok
Guest

Pre-Cal circle question

Question: Determine the radius and center of the circle represented by x^2+2x+y^2-2y-5=0

To help: SquareRoot[(x-h)^2 + (y-k)^2)]=r
&
(x-h)^2 + (y-k)^2=r^2

Of course my book has zero problems similar to this one. I am trying to get anything in the form of (x-h)^2 and the same with y and k. I can only pull x and y's out, which would take it out of general form, and still leave me with nothing.

Also is there anyway to graph circles? I use to know a way you could do half of one, then take the negative or something to get the other half. My exams tomorrow, but its multiple choice so if I can just look at the calculator I dont have to show anything.

Any helps greatly appreciated

Thanks.

Oh ya and (h,k) is the center of the circle

#2 2006-12-10 22:10:53

gnitsuk
Member
Registered: 2006-02-09
Posts: 121

Re: Pre-Cal circle question

We need to get

into the form

Here's how:

Look at the expansion of

which is

That looks a lot like the first two terms of our original equation viz

So we can clearly see that

Similarly we have

So we can re-write our original equation as:

and collect the constants together to give

So finally we have:

So our equation is that of a cricle with centre (-1,1) and radius

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#3 2006-12-10 22:17:56

gnitsuk
Member
Registered: 2006-02-09
Posts: 121

Re: Pre-Cal circle question

To graph the equation

Rearrange it as a quadratic in y, giving:

Now use the quadratic formula http://mathworld.wolfram.com/QuadraticEquation.html to solve this for y.

Here

And so we have:

So you can enter this into a graphing package and get the two halves of the circle.

Last edited by gnitsuk (2006-12-10 22:18:59)

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