I'm really bad at these types of questions, I don't know what it is about them but they always seem to stump me. Here it is,
The variable point is on the hyperbola with equation and N is the point (3a, 3b). The point Q lies on the line PN so that PQ = 2QN. As t varies find, in cartesian form, the locus of Q.
I tried to find the line PN by finding its gradient by
and then using the usual method for finding the equation of a straight line, that is
but then I get stuck and cannot see what to do next. Do I need to find the point Q? I know I need to eliminate t, but I just can't see how to approach this one.
Are there any general tips and tricks common to conic section questions like this? Given a formula I can identify which conic it is, and its directrix, foci etc. But when the questions get slightly harder (like this one) I just go to pieces.
Any help would be much appreciated