We study the magnetic properties and emergence of superconductivity in YBa_22Cu_33O_77 (YBCO)/ La_{0.67}0.67Sr_{0.33}0.33MnO_33 (LSMO) heterostructures. Bilayer films of superconducting layer, YBCO, and ferromagnetic layer, LSMO were grown on SrTiO_{3}3 (STO) (001) substrate using ultrahigh vacuum Pulsed Laser Deposition system. Magnetization data at 100 K as a function of applied magnetic field shows ferromagnetic behaviour due to the LSMO layer. Cooling below 100 K leads to superconductivity in this material; the onset of superconductivity occurs at a temperature, T_{c,SC},Tc,SC, of 86 K for H_{ext}\perp cHext⊥c (in-plane) & 84 K for H_{ext}||cHext||c (out-of-plane) under 100 Oe applied field. In-plane magnetic measurements show significant suppression of diamagnetic behaviour as compared to the out-of-plane measurements. The susceptibility signals are higher for out-of-plane direction. Such strong anisotropy in magnetism and the transition temperatures reveal complex interplay of magnetism and superconductivity in this system and calls for further study in this direction.