On this problem:
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.
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.
My steps so far have been substitutey+x=k into {(x^2)/a^2)}+ {(y^2)/(a^2)} and simpify it down to (b^2+a^2)x^2-2a^2kx+a^2k^2-a^2b^2=0. Can someone show me what to do from here? I really, really appreciate the help!
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.
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.
My steps so far have been substitutey+x=k into {(x^2)/a^2)}+ {(y^2)/(a^2)} and simpify it down to (b^2+a^2)x^2-2a^2kx+a^2k^2-a^2b^2=0. Can someone show me what to do from here? I really, really appreciate the help!