In this thesis, we consider isoparametric curves of quadratic F-B$acute{e}$zier curves. F-B$acute{e}$zier curves unify C-B$acute{e}$zier curves whose basis is {sint, cos t, t, 1} and H-B$acute{e}$zier curves whose basis is {sinht, cosh t, t,1}. Thus F-B$acute{e}$zier curves are more useful in Geometric Modeling or CAGD(Computer Aided Geometric Design). We derive the relation between the quadratic F-B$acute{e}$zier curves and the quadratic rational B$acute{e}$zier curves. We also obtain the geometric properties of isoparametric curve of the quadratic F-B$acute{e}$zier curves at both end points and prove the continuity of the isoparametric curve.