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

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frecklesBest ResponseYou've already chosen the best response.2
You know the distance formula?
 one year ago

frecklesBest ResponseYou've already chosen the best response.2
You want to maximize that using the points (1,0) and (x,y)
 one year ago

1aceBest ResponseYou've already chosen the best response.0
ok i know y^2=(100100x^2)
 one year ago

1aceBest ResponseYou've already chosen the best response.0
so d^2=x^2 + (100100x^2)^2
 one year ago

1aceBest 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)?
 one year ago

1aceBest ResponseYou've already chosen the best response.0
or am I just doing this all wrong? :\
 one year ago

frecklesBest 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)
 one year ago

frecklesBest ResponseYou've already chosen the best response.2
Okay and you squared the distance! Good job! :)
 one year ago

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

frecklesBest ResponseYou've already chosen the best response.2
\[100x^2+y^2=100 => y^2=100100x^2\]
 one year ago

frecklesBest ResponseYou've already chosen the best response.2
Why did you square y^2?
 one year ago

frecklesBest ResponseYou've already chosen the best response.2
\[d^2=(x1)^2+100100x^2\]
 one year ago

1aceBest ResponseYou've already chosen the best response.0
OOOHH omg hahaahah thats where i went wrong?!
 one year ago

1aceBest 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
 one year ago

frecklesBest ResponseYou've already chosen the best response.2
Nope nope.... So when you found ((x1)^2)' You used chain rule right?
 one year ago

frecklesBest ResponseYou've already chosen the best response.2
We know that (100)'=0
 one year ago

frecklesBest ResponseYou've already chosen the best response.2
(100x^2)'=100(x^2)' we know to use power rule here
 one year ago

1aceBest ResponseYou've already chosen the best response.0
yes so i get 2(x1)*1 + 0 200x
 one year ago

frecklesBest ResponseYou've already chosen the best response.2
You need to distribute that 2. 2(x1)=2x1(2)=2x2
 one year ago

frecklesBest ResponseYou've already chosen the best response.2
\[\text{ Set } (d^2)'=0\]
 one year ago

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

frecklesBest ResponseYou've already chosen the best response.2
Minimizing d^2 will give us the same results as minimizing d
 one year ago

1aceBest 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?
 one year ago

1aceBest ResponseYou've already chosen the best response.0
also i only get 1 answer, shouldnt there be another point also?
 one year ago

frecklesBest ResponseYou've already chosen the best response.2
\[y=\pm \sqrt{100100x^2} \text{ correct?}\]
 one year ago

1aceBest 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
 one year ago

frecklesBest ResponseYou've already chosen the best response.2
\[(\frac{1}{99}, \sqrt{100100(\frac{1}{99})^2}) \text{ and } (\frac{1}{99},\sqrt{100100(\frac{1}{99})^2})\]
 one year ago

1aceBest 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 ?
 one year ago

frecklesBest ResponseYou've already chosen the best response.2
dw:1353821740124:dw
 one year ago

frecklesBest ResponseYou've already chosen the best response.2
dw:1353821859781:dw
 one year ago

1aceBest ResponseYou've already chosen the best response.0
omg ok i see !!! i think i got it now !!!
 one year ago

frecklesBest ResponseYou've already chosen the best response.2
dw:1353821881622:dw
 one year ago

1aceBest ResponseYou've already chosen the best response.0
thank you !! i get it now !!
 one year ago
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