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Let k be a positive real number. The square with the vertices (k,0), (0,k), (-k,0), and (0,-k) are plotted on the coordinate plane.

 

 

Find conditions on a>0 and b>0 such that the ellipse \(\[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\]\)

 

is contained inside the square (and tangent to all of its sides)

 

HINTS: suppose that the line x+y=k is tangent to the ellipse \(\[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\]\)

 

Algebraically, what can we say about the solutions? In particular, the number of solutions?

 

A thourough explanation would be helpful. Thank you! 

 May 21, 2020
 #1
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What is an ellipse?

 
 May 21, 2020
 #2
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You can find more information here:

 

https://en.wikipedia.org/wiki/Ellipse

 

https://mathworld.wolfram.com/Ellipse.html

 
Guest May 21, 2020
 #3
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This is what an ellipse looks like:

 
Guest May 21, 2020
 #4
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This is what an ellipse looks like:

 

 
Guest May 21, 2020
 #5
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Let k be a positive real number. The square with the vertices (k,0), (0,k), (-k,0), and (0,-k) are plotted on the coordinate plane.

Find conditions on a>0 and b>0 such that the ellipse 

is contained inside the square (and tangent to all of its sides)

HINTS: suppose that the line x+y=k is tangent to the ellipse 

Algebraically, what can we say about the solutions? In particular, the number of solutions?

 

answer here: https://web2.0calc.com/questions/please-help-asap_141#r2

 

laugh

 
 May 22, 2020

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