# Math Help - A small hyperbola question

1. ## A small hyperbola question

a) if a comet travels along a hyperbola x^2/a^2 - y^2/b^2 = 1 and a planet locates at the focus (c,0), where c^2 = a^2 + b^2, find the closest distance that the comet ever comes to the planet. Give a sketch to illustrate the answer.

b) if a=b=1, find that distance.

2. The closest point is (a,0). A point on the hyperbola can be represented as $(a\cosh t, b\sinh t)$. The square of its distance from $(\sqrt{a^2+b^2},0)$ is $a^2\cosh^2t -a^2-b^2+b^2\sinh^2t$. Use calculus to find that this has its minimum value at t=0.