Given the two curve equations are: $(x-1)^2 + y^2 = 2$ and $(x+1)^2 + y^2 = 2$, prove that the two curves intersect orthogonally, then find the equation of the tangent at the intersection points.
What I did was differentiate both equations expecting the derivatives to be reciprocals of each other resulting in a $-1$, but instead I got $\frac{dy}{dx}^1 = -\frac{x-1}{y}$ and $\frac{dy}{dx}^2 = -\frac{x+1}{y}$. What should I do now?
Best Answer
You would have to calculate the tangent slopes at the point(s) of intersection