Disagree with your differentiation, firstly.
Anyway, you know that so substitute that into the original equation to find the value for x at this point. Then it becomes a case of substitution.
Sorry I typoed
Should have been
(x^2/36)+(y^2/64)=1
Forgive me, but I'm just not making a connection between the information y(1)=7.88811 and the original equation. I know I need to substitue and solve for x, but there's a point in my brain that doesnt want to accept how this should occur.
is it just plug in 7.88811 for y^2 and solve for x?