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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
We need to get
into the formHere's how:
Look at the expansion of
which isThat 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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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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