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!

Guest May 21, 2020

#5**+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?**

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

heureka May 22, 2020