The line PQ has the equation
or .
If the line passes through the focus, then we have
.
The coordinates of R are
.
Now, we have
Lol I seem to be stuck with a lot of questions to do with the parabola.
Q: Show that the normals at P (at^2, 2at) and Q (as^2,2as)on the parabola with equation y^2=4ax meet at the point R where the coordinates of R are
[a(t^2+ts+s^2+2)], -ats(t+s)]. This part of the question I've managed to do. It's the next part that I'm stuck on: Given that the line PQ passes through the focus S(a, 0), show that as t and s vary, R lies on the curve with equation y^2=a(x-3a).
I tried to eliminate the variables t and s, but was unsuccessful. Can someone help please?
Btw, can someone let me know what topic this post should come under for future reference?