Heat flows normal to isotherms, curves along which the temperature is constant. Find the line along which heat flows through the point $(2,5)$ when the isotherm is along the graph of $2x^2+y^2=33$.
Here it gives me the equation of the graph (original function). I know that by finding the derivative of the expression it gives I can substitute $x$ ($x=2$) in and solve for the slope. Then I can use $y = mx + b$ to get the equation of the line as it asks for.
However, it doesn't show the function in $f(x)$ form. Therefore, I'm told that I need to use Implicit Differentiation before I do anything. This is where I'm completely lost. I have no idea what Implicit Differentiation means and how to get this expression in $f(x)$ form so I can find the derivative. Can someone please guide me. I would appreciate it if you could comment on your steps so I can have a more intuitive understanding.