Ellipse and ellipsoid fitting has been extensively researched and has broad applications. Traditional ellipse fitting methods provide accurate estimation of ellipse parameters in the case of low noise. However, their performance is compromised when the noise level or the ellipse eccentricity are high. In this paper, an algorithm based on the geometric definition of an ellipse/spheroid (a special class of ellipsoid) is proposed. It performs well in high-noise, and high-eccentricity cases. The efficacy of the new algorithm is demonstrated through simulations.