Solve the problem.

Find an equation for the level curve of the function $f(x,y)={\displaystyle \underset{x}{\overset{y}{}}}tdt$ that passes through the point $(6,9).$

A$)y^2-x^2=-45$

B$)y^2+x^2=117$

C$)y^2-x^2=117$

D$)y^2-x^2=45$