The formula for an ellipse is x^2/a^2+y^2/b^2=1. The formula for the slope of an ellipse is y'(x)= - (x/a^2)/(y/b^2). Setting y'(x)=1, we have (x/a^2)/(y/b^2)=-1. Solving these two equations yields the solutions:
x = - a^2/sqrt(a^2+b^2), y= +b^2/sqrt(a^2+b^2),
and
x = +a^2/sqrt(a^2+b^2), y= -...