Hi, sorry question caused you pain. I have sent you an email with intended solution. Respectfully I think you went down the wrong route using vectors rather than parametric differentiation, then finding the equation of tangents at P and at Q, if let t=p at point P and t=q at point Q, find dy/dx, find equations of tangents at these points, use given fact that pq=-1, find coordinates of intersection, prove this point lies on the given curve. Sorry again for question, intended solution was not the algebra tedium you had to endure.
Now that you type this all out, it seems obvious that this is a better way to do it! I'm surprised I didn't scrap what I was doing and just do it the way you suggested.
![The most beautiful equation in math, explained visually [Euler’s Formula]](/img/1.gif)
Hi, sorry question caused you pain. I have sent you an email with intended solution. Respectfully I think you went down the wrong route using vectors rather than parametric differentiation, then finding the equation of tangents at P and at Q, if let t=p at point P and t=q at point Q, find dy/dx, find equations of tangents at these points, use given fact that pq=-1, find coordinates of intersection, prove this point lies on the given curve. Sorry again for question, intended solution was not the algebra tedium you had to endure.
Now that you type this all out, it seems obvious that this is a better way to do it! I'm surprised I didn't scrap what I was doing and just do it the way you suggested.