Find the unit normal to an ellipse given by an equation The equation of the ellipse is given as being: $$x^2 -xy + y^2 = 7$$We're instructed to find a unit normal to the curve at a general point $P(x,y)$, and also at point $(-1,2)$ in particular.
My intuition is that I need to parameterize this equation, but I have no idea how to go about doing that. I thought that once I had the parametric equations, I could take the derivative of that set of equations with respect to $t$, and get a general equation for the slope at any point. With that I could probably use the dot product to find the perpendicular normal.
That's my reasoning, but of course, I'm really unsure if any of that is correct. 

We have $2x-y-xy'+2yy'=0$ so $y' =\frac {y-2x} {2y-x}$. At any point $(x,y)$ on the ellipse the slope of the normal line is $\frac {2y-x} {2x-y}$. At $(-1,2)$ it is $-5/4$. (A unit vector along the normal is $(\frac 1 {\sqrt {1+m^{2}}},\frac m {\sqrt {1+m^{2}}})$ where $m$ is the slope). 
