formula to plot ( 1/4 eliptical) curve with only minx,miny and maxx,maxy

Question

Here is the curve i wish to plot with a function:

I expect the curve to be 1/4 of an elipse but I only have the coordinates to work with (minx,miny and maxx,maxy). I've been using the graphing tool at: http://itools.subhashbose.com/grapher but I haven't been able to remember way back to highschool when we worked on functions like these (it's been over 30 years). Any help greatly appreciated.

Note: answers come in quick, wish i had specified earlier the format of the equation ideally looks like: f(x) = ?

Answer 1

define $a=x_{max}-x_{min}$ and $b=y_{max}-y_{min}$

then you need to plot ...

$$ y=y_{max} - b\sqrt{1-\frac{(x-x_{min})^2}{a^2} } $$

from $x=x_{min}$ to $x=x_{max}$

Answer 2

If we let $$a=X_{max}-X_{min};\, b=Y_{max}-Y_{min};$$

then parametrically we can plot

$$ X= X_{min}+ a \cos t, Y= Y_{max} + b \sin t $$