SOLUTION: help needed: Give points which are outside and pont which are inside of the circles in this equation: x^2+y^2+6x=0 p.s: could you please explain the solution for me that I can so

Algebra ->  Circles -> SOLUTION: help needed: Give points which are outside and pont which are inside of the circles in this equation: x^2+y^2+6x=0 p.s: could you please explain the solution for me that I can so      Log On


   

Question 203863: help needed:
Give points which are outside and pont which are inside of the circles in this equation: x^2+y^2+6x=0
p.s: could you please explain the solution for me that I can solve a group of questions like this ? Thank you:)
Found 2 solutions by Alan3354, Earlsdon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Give points which are outside and pont which are inside of the circles in this equation: x^2+y^2+6x=0
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You need to find the center and the radius of the circle.
Put it into standard form,
(x-h)^2 + (y-k)^2 = r^2 where the center is at (h,k) and the radius is r.
x^2+y^2+6x=0
Complete the square for the x terms.
x^2 + 6x + 9 + y^2 = 9
(x+3)^2 + y^2 = 3^2
So the center is (-3,0) and the radius is 3.
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Assuming you mean all points inside and out:
Inside:
(x+3)^2 + y^2 <9
Outside:
(x+3)^2 + y^2 >9
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That's it. This one could have been shortcutted, but that might not apply in all cases. Changing the = to < and > might move the center of the circle.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First get your equation into the standard form for a circle whose center is at (h, k) and whose radius is r.:
%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2
x%5E2%2By%5E2%2B6x+=+0 Group the variables as shown below:
%28x%5E2%2B6x%29%2By%5E2+=+0 Now "complete-the-square" in the x-variable by adding the square of half the x-coefficient to both sides of the equation. %286%2F2%29%5E2+=+9
%28x%5E2%2B6x%2B9%29%2By%5E2+=+0%2B9 Factor the trinomial in x.
%28x%2B3%29%5E2%2By%5E2+=+9 Compare this with the standard form for a circle:
%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2
The center of the circle is at (-3, 0) and the radius is 3.
It's probably easier to graph the circle then pick out the appropriate points inside and outside of the circle.
To graph the circle, you will need to solve your equation for y (you will get two solutions) then graph both solutions.
x%5E2%2By%5E2%2B6x+=+0 Subtract x%5E2 and 6x from both sides.
y%5E2+=+-x%5E2-6x Take the square root of both sides.
y+=+sqrt%28-x%5E2-6x%29 and y+=+-sqrt%28-x%5E2-6x%29
Now we'll graph these two solutions on the same grid:
graph%28400%2C400%2C-8%2C8%2C-8%2C8%2Csqrt%28-x%5E2-6x%29%2C-sqrt%28-x%5E2-6x%29%29