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plz help asap im really confused

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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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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
+24949
+1

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?

May 22, 2020