The English physiologist Archibald Vivian Hill proposed, in his studies, that the velocity $v$ of contraction of a muscle when subjected to a weight $p$ is given by the equation $( p + a )( v + b ) = K$, with $a$, $b$, and $K$ constants.
A physiotherapist, with the intention of maximizing the beneficial effect of the exercises he would recommend to one of his patients, wanted to study this equation and classified it as follows:
| Type of curve |
| Oblique half-line |
| Horizontal half-line |
| Branch of parabola |
| Arc of circle |
| Branch of hyperbola |
The physiotherapist analyzed the dependence between $v$ and $p$ in Hill's equation and classified it according to its geometric representation in the Cartesian plane, using the coordinate pair ($p$; $v$). Assume that $K > 0$.
The graph of the equation that the physiotherapist used to maximize the effect of the exercises is of the type
(A) oblique half-line.
(B) horizontal half-line.
(C) branch of parabola.
(D) arc of circle.
(E) branch of hyperbola.