How does an ellipse compare with a perfect circle?

Answer 1

The question is a strange one as the answer depends on the context in which the question is asked. Graphically speaking: A line forming a perfect circle means that given a set point as the centre of the circle, the line will always be the exact same distance from the centre of the circle at any point along the line. An Ellipse on the other hand is a smooth closed curve that is symmetrical about its centre point, or by way of example, two points on the ellipse which are exactly opposite each other across the centre of the ellipse will each be exactly the same distance from the centre. Mathematically speaking, the difference can be defined by the equations (formulae) of each: A perfect Circle will have the equation: (x-a)2 + (y-b)2 = r2 for a circle with: a centre in Cartesian co-ordinates of (a,b)

a radius of r

An Ellipse will have the equation: (x2/a2) + (y2/b2) = 1 for an ellipse with: a maximum value in the X-axis of 'a' (+a or -a)

a maximum value in the Y-axis of 'b' (+b or -b) The essential difference in these equations can be seen if we consider an ellipse and a circle each with a centre of (0,0) in Cartesian co-ordinates. the equation for a circle would become: X2 + Y2 = r we can manipulate this equation by dividing both sides by 'r' to give X2/r + Y2/r = 1 the only difference now between the equation of the ellipse and this equation of a circle is that instead of allowing the 'r' X2/r to be different to the 'r' in Y2/r as in the case of an ellipse, both are kept the same.