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

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ok i know y^2=(100100x^2)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so d^2=x^2 + (100100x^2)^2

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0or am I just doing this all wrong? :\

freckles
 3 years ago
Best 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)

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

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

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

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0OOOHH omg hahaahah thats where i went wrong?!

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

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

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

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

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

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

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ok, so i get x=1/98 ?

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0also i only get 1 answer, shouldnt there be another point also?

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

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

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0omg ok i see !!! i think i got it now !!!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0thank you !! i get it now !!
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