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1ace
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Find the points on the ellipse 100x^2+y^2=100 that are farthest away from the point (1,0)
 2 years ago
 2 years ago
1ace Group Title
Find the points on the ellipse 100x^2+y^2=100 that are farthest away from the point (1,0)
 2 years ago
 2 years ago

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freckles Group TitleBest ResponseYou've already chosen the best response.2
You know the distance formula?
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
You want to maximize that using the points (1,0) and (x,y)
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
ok i know y^2=(100100x^2)
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
so d^2=x^2 + (100100x^2)^2
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
but im not sure about the x^2 part is it (1x)^2 because the point is (1,0)?
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
or am I just doing this all wrong? :\
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
\[d=\sqrt{(\Delta x)^2+(\Delta y)^2}=\sqrt{((x1)^2+(y0)^2}=\sqrt{(x1)^2+y^2}\] I used the points given (1,0) and (x,y)
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
Okay and you squared the distance! Good job! :)
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
\[d^2=(x1)^2+y^2\] Replace y^2 with what you found :)
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
yep i did that ! :o
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
\[100x^2+y^2=100 => y^2=100100x^2\]
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
Why did you square y^2?
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
\[d^2=(x1)^2+100100x^2\]
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
OOOHH omg hahaahah thats where i went wrong?!
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
so then after i take the derivative is do i find the roots ? 199x1=0? that doesnt seem right :s
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
Nope nope.... So when you found ((x1)^2)' You used chain rule right?
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
We know that (100)'=0
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
(100x^2)'=100(x^2)' we know to use power rule here
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
yes so i get 2(x1)*1 + 0 200x
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
You need to distribute that 2. 2(x1)=2x1(2)=2x2
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
\[\text{ Set } (d^2)'=0\]
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
\[2x2200x=0\]
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
ok but dont i have to divide by the 2d from when i differentiate (d^2)'
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
Minimizing d^2 will give us the same results as minimizing d
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
ok, so i get x=1/98 ?
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
then would that be my point? x= 1/98 and subbing that into the original equation y= 9.99948?
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
also i only get 1 answer, shouldnt there be another point also?
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
\[y=\pm \sqrt{100100x^2} \text{ correct?}\]
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
Say yes. lol
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
but my x is only 1 point? and my y's will be 2 points? sorry im just a little confused
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
\[(\frac{1}{99}, \sqrt{100100(\frac{1}{99})^2}) \text{ and } (\frac{1}{99},\sqrt{100100(\frac{1}{99})^2})\]
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
okay but why 1/99? i thought we found that 2x2200x=0 then wouldnt x be 2/198 ?
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
dw:1353821740124:dw
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
\[198/2=99\]
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
\[2/198=1/99\]
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
dw:1353821859781:dw
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
omg ok i see !!! i think i got it now !!!
 2 years ago

freckles Group TitleBest ResponseYou've already chosen the best response.2
dw:1353821881622:dw
 2 years ago

1ace Group TitleBest ResponseYou've already chosen the best response.0
thank you !! i get it now !!
 2 years ago
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