The closest point is (a,0). A point on the hyperbola can be represented as . The square of its distance from is . Use calculus to find that this has its minimum value at t=0.
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.