College Algebra question.?

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Hiiii. The equation for a circle is as following:

(x-a)^2 + (y-b)^2 = r^2

r is the radius and the (a,b) is the coordinates of the center.

So we need to get your equation in the form shown above. :]

x^2 + y^2 - 10x +4y +20 = 0

= (x^2 - 10x) + y^2 + 4y = -20

Note: I just flipped the 10x and y^2. Then I took 20 to the other side.

= (x^2 - 10x +25) + (y^2 + 4y + 4) = 9

Note: I added 29 to both sides! Why did I add 29? Because I am trying to get the equation in the form (x-a)^2 + (y-b)^2 = r^2
Therefore I have to do some factoring!

= (x-5)^2 + (y+2)^2 = 9

Note: But 9 is not in the form r^2! So we have to factor.

= (x-5)^2 + (y+2)^2 = 3^2

Note: Now match this equation with your formula!

(x-a)^2 + (y-b)^2 = r^2
= (x-5)^2 + (y-(-2))^2 = 3^2

r=3
a=5
b=-2

Radius is 3. Coordinates of center are (5,-2)!

I'm sorry if this is hard to understand. :[ But i hope i helped in some way. :]...Show more

ok i have to do this kind of thing all the time in multivariable calculus...you have to first move the 20 over to the right to get

x^2 - 10x + y^2 +4y = 20

i also rearranged it to make the next part easier...next, you have to do what's called completing the square on the left...you kinda add numbers to the left side from the right so you can factor...i'll do it and then explain

x^2 - 10x + 25 + y^2 + 4y + 4 = 9

ok, so if you look at what i have now, you can factor the left side to get

(x - 5)^2 + (y + 2)^2 = 9

you can see by taking a total of 29 from the right side and moving it to the left side, you end up with 9 on the right side and 25 and 4 on the left...then you can simplify the left side by factoring...then, you just look at the equation and the square root of the right side is the radius, so that would be 3, and the center would be the x and y numbers that would make the two things in parentheses equal to 0, so the center would be (5,-2)...Show more

x^2 - 10x + y^2 + 4y = -20
complete the squre of both the x and y terms:
(x^2 - 10x + 25) + (y^2 + 4y + 4) = -20 + 25 + 4
(x - 5)^2 + (y + 2)^2 = 9

center (5,-2), radius 3...Show more