Hello uselessjackThe difference between the distances AP and PB is miles.

The equation of a North-South opening hyperbola, centre the origin, is of the formB) Find an equation for the branch of the hyperbola indicated in red in the figure, using miles as the unit of distance.

and the absolute difference between the distances of any point on the hyperbola from the foci is . So here, .

The foci are at . So

But

Can you finish off now?

Grandad