# A small hyperbola question

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.