Question 1068651
So choose a coordinate system so that the center of the road is (0,0).
The left side of the road is then (-6,0) and the right is (6,0).
The far left of the left sidewalk is (-8,0) and the far right of the right sidewalk is (8,0).
The points (-6,3.6) and (6,3.6) must be on your ellipse.
To make it the smallest ellipse, (-8,0) and (8,0) must also be on your ellipse.
Start with the general equation of an ellipse.
{{{x^2/a^2+y^2/b^2=1}}}
(8,0)
{{{8^2/a^2+0^2/b^2=1}}}
{{{a^2=64}}}
{{{a=8}}}
.
.
.

(6,3.6)
{{{x^2/a^2+y^2/b^2=1}}}
{{{(6/8)^2+(3.6/b)^2=1}}}
{{{(3/4)^2+(3.6/b)^2=16/16}}}
{{{(3.6/b)^2=16/16-9/16}}}
{{{(3.6/b)^2=7/16}}}
{{{7b^2=16(3.6)^2}}}
{{{7b^2=16(18/5)^2}}}
{{{7b^2=5184/25}}}
{{{b^2=5184/175}}}
So when, {{{x=0}}}
{{{y[max]^2/b^2=1}}}
{{{y[max]^2=b^2}}}
{{{y[max]=b}}}
{{{y[max]=sqrt(5184/175)}}}
{{{y[max]=(72/35)sqrt(7)}}}{{{m}}}
.
.
.
*[illustration g23.JPG].