Difference Between Circle and Ellipse

Circle vs Ellipse

Both ellipse and circle are closed two-dimensional figures, which are referred as conic sections. A conic section is formed when a right circular cone and a plane intersect. There are four conic sections: circle, ellipse, parabola and hyperbola. The conic section type depends on the angle between the plane and the axis of the cone.

Ellipse

An Ellipse is the locus of a point that moves so that the sum of the distances between the point and two other fixed points is constant. These two points are called foci of the ellipse. The line joining these two foci is called the major axis of the ellipse. The midpoint of the major axis is called the center of the ellipse. A line perpendicular to the major axis and passes through the center is called the minor axis of the ellipse. These two are the diameters of the ellipse. The major axis is the longer diameter, and the minor axis is the shorter diameter. One-half of the major and the minor axis are known as the semi-major axis and the semi-minor axis, respectively.

The standard formula of an ellipse with vertical major axis and a center (h, k) is [(x-h)²/b²] + [(y-k)²/a²] =1, where 2a and 2b are the lengths of major axis and minor axis respectively.

Circle

The circle is the locus of a point, which moves with an equidistance from a given fixed point. The distance between any point on the circle and its center is constant, which is known as the radius. A circle is formed when a plane intersect a cone, perpendicular to its axis.

The circle is a special case of the ellipse where a=b=r, in the equation of the ellipse. ‘r’ is the radius of the circle. Therefore, by substituting a and b by r; we get the standard equation of a circle with radius r and the center (h, k): [(x-h)²/r²] + [(y-k)²/r²] =1 or (x-h)²+(y-k)² = r².