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!
+26367 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
