Past exam of the physics 1 paper of the University of Oxford / 2016 / 10 / ii

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,Both old and new velocities are tangential there, so the required first impulse is prograde, with