Methods used to detect giant exoplanets can be broadly divided into two categories: indirect and direct. Indirect methods are more sensitive to planets with a small orbital period, whereas direct detection is more sensitive to planets orbiting at a large distance from their host star. %, and thus on long orbital period. This dichotomy makes it difficult to combine the two techniques on a single target at once. Simultaneous measurements made by direct and indirect techniques offer the possibility of determining the mass and luminosity of planets and a method of testing formation models. Here, we aim to show how long-baseline interferometric observations guided by radial-velocity can be used in such a way. We observed the recently-discovered giant planet $beta$ Pictoris c with GRAVITY, mounted on the Very Large Telescope Interferometer (VLTI). This study constitutes the first direct confirmation of a planet discovered through radial velocity. We find that the planet has a temperature of $T = 1250pm50$,K and a dynamical mass of $M = 8.2pm0.8,M_{rm Jup}$. At $18.5pm2.5$,Myr, this puts $beta$ Pic c close to a hot start track, which is usually associated with formation via disk instability. Conversely, the planet orbits at a distance of 2.7,au, which is too close for disk instability to occur. The low apparent magnitude ($M_{rm K} = 14.3 pm 0.1$) favours a core accretion scenario. We suggest that this apparent contradiction is a sign of hot core accretion, for example, due to the mass of the planetary core or the existence of a high-temperature accretion shock during formation.
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