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anonymous
 one year ago
Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.
x2 + 2x + y2 + 4y = 20
I am completely lost on how to do this!!! I will fan and medal please someone help!
anonymous
 one year ago
Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit. x2 + 2x + y2 + 4y = 20 I am completely lost on how to do this!!! I will fan and medal please someone help!

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 @zepdrix @mathmate

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Complete the square for x and y, then you'll get the equation of the circle with centre (h,k) and radius r as in (xh)^2+(yk)^2 = r^2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2@cheetah21 Can you do that or do you need further help?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I do need further help..sorry im just really bad with math :/

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Start with the given equation, we need to transform it to the standard form of the circle, then we can identify (by comparison) h,k and r.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay how do we do that ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2The given equation is: x2 + 2x + y2 + 4y = 20 After adding a 1 and a 4 on both sides, we put the equation as (x^2+2x+1) + (y^2+2(2y)+4) = 20 +1 +4 It's still the same equation, but what are in the parentheses are perfect squares. Can you factor the two expressions in parentheses?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x2 + 2x + y2 + 4y = 20 (x2 + 2x) + (y2 + 4y) = 20

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2I already put them in perfect squares, you don't need to simplify them. In fact: (x^2+2x+1) + (y^2+2(2y)+4) = 20 +1 +4 is the same as: (x+1)^2 + (y+2)^2 = 25 You can check to make sure by expanding the squares.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh okay im sorry , i was confused i guess :/ so now do we need to solve in the parentheses or what ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Next step is easy: you compare (x+1)^2 + (y+2)^2 = 5^2 with the standard form of the circle with centre (h,k) and radius r (xh)^2+(yk)^2 = r^2 and decide what the values of h, k and r are.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(Xh)^2 + (y  K)^2 = r^2 (xh)^2+(yk)^2 = r^2 is that what it should look like right now ?? and how do we figure out values ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Compare term by term, for example, (x+1)^2 = (xh)^2, what would be the value of h to make the right hand side (x+1)^2?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Would that be 1 also?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2If h=1, then we have (x+1)^2 on the left hand side, and (x1)^2 , so the two sides don't equal. You need to find another value of h.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so then that would be 2 ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2If h=2, then we have (x+1)^2 on the left hand side, and (x2)^2 , so the two sides don't equal. Remember we are looking for h in: (x+1)^2 = (xh)^2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2(x+1)^2 = (x4)^2 (are they equal?)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2There is a positive sign on the left, and a negative sign on the right, so h must be negative to make the two sides match, remembering (1)=+1. so putting h=1 will make (x+1)^2 = (x(1))^2=(x+1)^2 or both sides equal.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Can you try finding k from: (y+2)^2 = (yk)^2 ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2You would take the square root on both sides, so (y+2) = yk, can you solve for k?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(3) = yk 3yk Im sorry if thats a dumb answer i just dont know

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2From (y+2) = yk, subtract y from both sides, so yy+2 = yyk or 2=k, multiply by 1 to get 2=k, so we have h=1, k=2, and r=5 From the standard equation of a circle, (xh)^2+(yk)^2=r^2 we therefore found centre = (h,k)=1,2, and radius = r =5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait so thats the answer to the eqaution ? oh okay , well if i put all the stuff we have come up with together can you tell me if its in the correct order?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2put it up, and perhaps someone else will look at it for you. I have to go now, sorry! :(

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Its okay, thank you for all your help!
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