1. An arc detecting apparatus comprising: a memory; and a processor coupled to the memory, and configured to acquire an image data, approximate shapes included in the image data by straight lines, determine whether adjacent straight lines, among straight lines, form an arc shape, on a basis of positions of the adjacent straight lines and angles of the adjacent straight lines, detect the adjacent straight lines, when it is determined that the adjacent straight lines form the arc shape, detect, on a basis of positions of arcs detected, an ellipse including the detected arcs, and determine to which positions of the ellipse the arcs detected correspond, and when a number of portions of the ellipse which are determined to correspond to the determined positions is greater than or equal to a threshold, determine that a combination of the arcs corresponding to the given positions is an ellipse.