To find the slope, we can use implicit differentiation:
We can find the value of the slope of the tangent line at the point :
The slope of the normal line would be .
Thus, the tangent line has the form
At the point , the equation of our tangent line is
The normal line has the form
At the point , the equation of our normal line is
I take that back. The tangent line is perpendicular to the normal line [and the normal line happens to pass through the origin].I don't think so. From what I see, the lines don't pass through the origin.
I hope that this makes sense!