Question 875136
Those tell you that a=10, {{{c=(8-(-2))/2=5}}}, and center is (4,3).


The relationship among a, b, and c, is {{{b^2+c^2=a^2}}}, meaning {{{b^2=a^2-c^2}}}.


The standard form equation which you still need to finish, is:
{{{highlight_green((y-3)^2/100+(x-4)^2/b^2=1)}}}.
Notice carefully how a and b are positioned.  The MAJOR axis and vertices are vertical.



<s>I KNOW I made a mistake there, but I will leave this solution up anyway.  Maybe I will find the mistake...</s>(Mistake found and corrected).