SOLUTION: Let k be a positive real number. The square with vertices (k,0), (0,k), (-k,0), and (0,-k) is plotted in the coordinate plane. It is possible to draw an ellipse so that it is tang

Question 1172911: Let k be a positive real number. The square with vertices (k,0), (0,k),
(-k,0), and (0,-k) is plotted in the coordinate plane. It is possible to draw an ellipse so that it is tangent to all sides of the square; several examples are shown below.
(https://latex.artofproblemsolving.com/6/e/6/6e67d2c4f7235dab1e7d931aa1228b4ef76678e2.png)
Find necessary and sufficient conditions on a > 0 and b > 0 such that the ellipse
{x^2}/{a^2} + {y^2}/{b^2} = 1 is contained inside the square (and tangent to all of its sides).
Make sure to prove that your conditions are both necessary (the ellipse being tangent to all the square's sides implies your conditions) and sufficient (your conditions imply the ellipse being tangent to all the square's sides).
Answer by ikleyn(52842) (Show Source): You can put this solution on YOUR website!

RELATED QUESTIONS
For this question, (Let k be a positive real number. The square with vertices (k,0),... (answered by Edwin McCravy)

concept check for f(x) = a(x-h)^2+k, in what quadrant is the vertex if (a) h>0, k>0; (b)... (answered by josgarithmetic)

Find k such that the equation x^2 - kx + 4 = 0 has a repeated real solution. Let me... (answered by ikleyn)

Let K be a real number, and consider the quadratic equation (k+1)x^2+4kx+2=0 a. Show... (answered by robertb)

Consider the following system of equation: 3x-4y=0 and 4x-5y=k where k is a constant Real (answered by josgarithmetic)

1(a): If k=(x-1)�/x�+4,where k is a real number, show clearly that (k-1)x�+2x+(4k-1)=0 (answered by solver91311)

x+y=k x-y=k the solution to the system shown is (0,k) (2,2)... (answered by stanbon)

Given that the equation {{{kx^2+12x+k=0}}} where k is a positive constant and has equal... (answered by lynnlo,vleith)

Let k be a positive real number. The line x + y = k/2 and the circle x^2 + y^2 = 3x - 6y... (answered by CPhill)