Recently I found an interesting exercise in my book that I can't solve and there's not a step-by-step solution for it in my book.
Calculate angle between an ellipse $\frac{x^2}{9}+\frac{y^2}{4} = 1 $ and circle $x^2+2x+y^2-4 = 0$ (or more precise, the angle between their tangents).
I've tried everything but can't do anything useful. How do I solve this easily?
On
Without calculations: the circle has its center at $O=(-1,0)$ and intersects the ellipse at the endpoints of the minor axis, $T=(0,\pm2)$. At $T$ the ellipse has horizontal tangent and the slope of radii $OT$ are $\pm2$. Hence the slope of the tangent is $\mp1/2$, which is also the tangent of the requested angle.
Sorry for being too lazy to type it all out. And also for the tiny (and bad) handwriting.
