The normal to the rectangular hyperbola xy=c squared, at the point P(ct, c/t), has equation y=tsquaredx + c/t -ct cubed.
The normal to the hyperbola at P meets the hyperbola again at the point Q. Find in terms of t the co-ordinates of Q.

halp?

Question

The normal to the rectangular hyperbola xy=c squared, at the point P(ct, c/t), has equation y=tsquaredx + c/t -ct cubed.
The normal to the hyperbola at P meets the hyperbola again at the point Q. Find in terms of t the co-ordinates of Q.

halp?

anonymous · Answer

$$Hyperbola: xy=c ^{2}$$
$$Normal of hyperbola: y=t ^{2}x + \frac{ c }{ t } - ct ^{3}$$
There's the equations written properly!