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Babynini
 one year ago
Identity and graph, Hyperbola?
Babynini
 one year ago
Identity and graph, Hyperbola?

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1it's not a hyperbola you can use something like geogebra (which is what I just used) or desmos to check https://www.geogebra.org/ https://www.desmos.com/calculator

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yep it's an ellipse

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1fabulous, so...what next? I grouped stuff and factored out but i'm not sure how to finish the squares.

Babynini
 one year ago
Best ResponseYou've already chosen the best response.14(x^28x ) 25(y^2+6y )=189

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the x coordinate is 8 cut that in half to get 4 then square it to get 16 you will add and subtract 16 inside the parenthesis \[\Large 4(x^28x \ \ \ \ \ \ \ \ ) + 25(y^2+6y \ \ \ \ \ \ \ \ )=189\] \[\Large 4(x^28x {\color{red}{+1616}} ) + 25(y^2+6y \ \ \ \ \ \ \ \ )=189\] the +1616 is to make sure that the expression doesn't change (since we're effectively adding 0). Then notice how x^28x+16 factors to (x4)^2

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1so now we've got 4(x4)^2 ?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1and is the right side 25(x3)^2

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1(sorry, by right I meant the y stuff)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you're forgetting about the 16 in the parenthesis

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large 4(x^28x + \underline{ \ \ \ \ \ \ \ \ } \ ) + 25(y^2+6y + \underline{ \ \ \ \ \ \ \ \ } \ )=189\] \[\Large 4(x^28x+1616) + 25(y^2+6y + \underline{ \ \ \ \ \ \ \ \ } \ )=189\] \[\Large 4((x^28x+16)16) + 25(y^2+6y + \underline{ \ \ \ \ \ \ \ \ } \ )=189\] \[\Large 4((x4)^216) + 25(y^2+6y + \underline{ \ \ \ \ \ \ \ \ } \ )=189\] \[\Large 4(x4)^264 + 25(y^2+6y + \underline{ \ \ \ \ \ \ \ \ } \ )=189\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what goes in the blank for the y terms?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah +99 goes in the blank on line 1 for the y terms

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1be careful it is NOT y^2  6y it's y^2 + 6y

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so you should have this \[\Large 4(x4)^264 + 25(y+3)^2  225=189\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1yeah. ok so since we're adding and doing stuff to the left side we need to do the same on the right, yeah?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1that's why I had +16 and 16 to balance things out

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1same for +99

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1oh! that's fabulous :) I was wondering because in class I remember the +9 but and doing stuff to the left side also but I like this better haha

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1well you could add things to both sides, but you'd have to be careful

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1Yep yep. So now what do we do?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1add 64 and 225 to both sides?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1so 100 on the right side :P

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1then divide the whole thing by 100 so we get 0 on the right again?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you mean 1 on the right side

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ 4(x4)^2 }{ 100 }+\frac{ 25(y+3)^2 }{ 100 }=1\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1and you can rewrite that into \[\Large \frac{(x4)^2}{25} + \frac{(y+3)^2}{4} = 1\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1so now we get all the other stuff from there?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah you can find the center, foci, vertices, covertices, etc

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1how did you get c?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1http://www.mathwarehouse.com/ellipse/images/formulfocus.gif

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1kks, and then the ellipse will be sideways yeah?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1so foci: \[(0,\pm \sqrt{21})\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the foci will shift along with the center

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433386754426:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433386763450:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433386776494:dw

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1so we've got to find the center first.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1in this case, the major axis is horizontal, so the foci + center all lay on the same horizontal level. Only the x values will change

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1oh nearly forgot the vertices dw:1433387027602:dw

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1wouldn't want to forget those! :P

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1ok. that makes sense.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1for vertical ellipses (where b > a) \[\Large \frac{(xh)^2}{a^2} + \frac{(yk)^2}{b^2} = 1\] we have this schematic dw:1433387213931:dw

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1this one isn't horizontal? o.0

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1no I'm saying IF it were vertical, then you'd have what you see above

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the ellipse you have is horizontal, like this dw:1433387651593:dw

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1so how do we find the center? :)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1Compare \[\Large \frac{(x4)^2}{25} + \frac{(y+3)^2}{4} = 1\] with \[\Large \frac{(xh)^2}{a^2} + \frac{(yk)^2}{b^2} = 1\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1The center of \[\Large \frac{(xh)^2}{a^2} + \frac{(yk)^2}{b^2} = 1\] is (h,k)

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1so foci : (4 sq21, 3) , (4sq21, 3)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I think you meant to say \[\Large \left(4 {\color{red}{ \textbf{+}}}\sqrt{21},3\right)\] for the second focus

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you have the correct foci

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1haha yay! Ok, vertex: (+/5, 3) ?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1did you mean \[\Large \left(4 \pm 5, 3\right)\]??

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1Length of major axis: 2a? minor axis 2b?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1only because a > b

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1so major: 50 minor: 8

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1lol I did (a^2)2 major = 10

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1major is 10, yep

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1minor isn't 8

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yep minor = 4

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1everything is perfect

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1thanks so much! a thousand medals for your efforts :)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you're welcome
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