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Godlovesme
 one year ago
HELPPPPPP ASAP PLEASE!! D:
Using the following equation, find the center and radius of the circle.
x2 + 2x + y2 + 4y = 20
Godlovesme
 one year ago
HELPPPPPP ASAP PLEASE!! D: Using the following equation, find the center and radius of the circle. x2 + 2x + y2 + 4y = 20

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acxbox22
 one year ago
Best ResponseYou've already chosen the best response.0http://www.regentsprep.org/regents/math/algtrig/atc1/circlelesson.htm

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.0sorry i gtg ^ that links explains what you have to do

Godlovesme
 one year ago
Best ResponseYou've already chosen the best response.1its ok i'll try to figure it out thanks tho :)

Godlovesme
 one year ago
Best ResponseYou've already chosen the best response.1@pooja195 help me please :((

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3you need to transform this equation:\[x^2 + 2x + y^2 + 4y = 20\]into the standard form:\[(xh)^2+(yk)^2=r^2\]which gives a circle of radius \(r\) and center at \((h,k)\)

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3start by looking at just the terms involving \(x\), i.e.:\[x^2+2x\]can you transform this into a form like \((x+?)^2\)?

Godlovesme
 one year ago
Best ResponseYou've already chosen the best response.1i'll try, sorry im not good at this

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3we know that:\[(x+a)^2=x^2+2ax+a^2\]

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3and we want to get:\[x^2+2x\]

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.0well like the website says, you need to transform it into the center radius form by completing the square

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3can you see what value of \(a\) we need to pick?

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.0nvr mind i will let @asnaseer explain :P

Godlovesme
 one year ago
Best ResponseYou've already chosen the best response.1what do u mean @asnaseer

Godlovesme
 one year ago
Best ResponseYou've already chosen the best response.1thanks though :)) @acxbox22

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3we know that:\[(x+a)^2=x^2+2ax+a^2\]can you see what value of \(a\) we need to pick so that we get a \(2x\) in the expansion on the righthandside?

Godlovesme
 one year ago
Best ResponseYou've already chosen the best response.1phew than God i felt so stupid lol

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3so we know that:\[(x+1)^2=x^2+2x+1\]agreed so far?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3but we need just \(x^2+2x\), so we need to subtract 1 from both sides to get:\[(x+1)^21=x^2+2x\]agreed?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3i.e. we know:\[(x+1)^2=x^2+2x+1\]\[\therefore (x+1)^21=x^2+2x+11=x^2+2x\]

Godlovesme
 one year ago
Best ResponseYou've already chosen the best response.1ohhh so now we're left with \[x^2+2x\] ?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3now remember your original equation was:\[x^2 + 2x + y^2 + 4y = 20\]we can now substitute \(x^2+2x\) with the new expression we found to get:\[(x+1)^21+y^2+4y=20\]understand?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3good, now lets first simplify this by adding 1 to both sides to get rid of the 1 from the lefthandside

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3\[(x+1)^21+y^2+4y=20\]\[\therefore (x+1)^21+y^2+4y+1=20+1\]\[(x+1)^2+y^2+4y=21\]following so far?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3great! so now we have:\[(x+1)^2+y^2+4y=21\]lets now concentrate on the terms involving \(y\), we have:\[y^2+4y\]here again we know that:\[(y+b)^2=y^2+2by+b^2\]so can you think of what value we need for \(b\) so that the \(2by\) term becomes \(4y\)?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3so we now have:\[(y+2)^2=y^2+4y+4\]but we are after just \(y^2+4y\), so we need to subtract 4 from both sides, i.e.:\[(y+2)^2=y^2+4y+4\]\[\therefore (y+2)^24=y^2+4y+44=y^2+4y\]agreed?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3ok, now recall we originally were given:\[x^2 + 2x + y^2 + 4y = 20\]which we transformed using \((x+1)^21=x^2+2x\) into:\[(x+1)^2+y^2+4y=21\]and now we also know that:\[(y+2)^24=y^2+4y\]so if we now replace \(y^2+4y\) with the new expression we just found for it, then we get:\[(x+1)^2+(y+2)^24=21\]agreed?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3now again we can simplify this bu adding 4 to both sides as follows:\[(x+1)^2+(y+2)^24=21\]\[\therefore (x+1)^2+(y+2)^24+4=21+4\]\[\therefore (x+1)^2+(y+2)^2=25\]

Godlovesme
 one year ago
Best ResponseYou've already chosen the best response.1i get it now!! so the center will be (1,2) and the radius will be 5? :D

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3perfect! I was going to add one more step saying you have to be careful now as we are trying to get to this form:\[(xh)^2+(yk)^2=r^2\]so we must rewrite our equation as:\[(x(1))^2+(y(2))^2=5^2\]but I guess you beat me to it! :D

Godlovesme
 one year ago
Best ResponseYou've already chosen the best response.1OMG THANK YOU SO MUCHHH!!!! you're a life saver, i really appreciate your help :))) <3

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3yw my friend. I really appreciate people who are genuinely interested in learning  keep up the good work! :)

Godlovesme
 one year ago
Best ResponseYou've already chosen the best response.1ahh you're awesome!! I spend more than an hour trying to figure this out lol u solved it in less that half an hour XD

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.3ok, bye for now  take care my friend :)
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