= Solution
For the <Hohmann transfer orbit>, the inner and outer circular radii are the ellipse's <pericentre> and <apocentre> distances, so $a=(r_0+r_1)/2$. The <vis-viva equation> gives the transfer speed at the inner tangent point,
$$
v_p=\sqrt{\frac\mu{r_0}}\sqrt{\frac{2r_1}{r_0+r_1}}.
$$
Both old and new <velocities> are tangential there, so the required first impulse is prograde, with
$$
\boxed{\Delta v_1=\sqrt{\frac\mu{r_0}}\left(\sqrt{\frac{2r_1}{r_0+r_1}}-1\right).}
$$
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