We present a novel method for fitting an ellipse to scattered data based on least-squares minimization. The new technique has several advantages over the standard ellipse fitting techniques. For one, it is constraint-free and computationally inexpensive thus making it easy to implement. Also, despite the absence of constraints, execution of the model always results in an ellipse fit. Additionally, the model results in a singular solution for a given set of datapoints. The proposed model is compared with standard techniques and shown to have the ability to fit an accurate ellipse even when other methods either fail to be ellipse-specific or take up excessive computation time for execution. An application to the problem of segmentation of the optic cup in retinal fundus images, is also presented. Experimental validation and performance comparisons show that the proposed technique is competitive with the state-of-the-art methods.