Ellipse

Euclid first propounded the ellipse and the name ellipse in Math was given by Apollonius. In the year 1602, Kepler believed that the mars’s orbit is of oval shape, later he noticed that it was forming an ellipse with the sun as focus. We can define the term ellipse as any closed curved figure or oval shaped figure and the sum of its distances from any focii (plural form of focus) to each and every line must be constant. Things which are in the shape of ellipse are termed as 'elliptical'. There are two focus points which define an ellipse, like two lines such as ‘p’ and ‘q’, these two focus lines are generator lines. Sometimes the lines are also known as ‘generatrix’. If the generator lines are at the same location then the figure formed will not be an ellipse it will be the Circle and circle is a special case of ellipse.

The midpoint inside the ellipse which links both the ‘generatrix’ is its Centre. The major axis and minor axis is the longest and shortest Diameter of ellipse. Here also like circle the perimeter of ellipse is known as circumference. The Line Segment which is linking any two points on ellipse is its Chord. Tangent is a line passing through an ellipse touching any one Point.

As discussed above that circle is the special case of ellipse. If we take both minor and major axis of same length the closed figure formed will be circle. Ellipse can also be defined by using its formula. The ellipse at its origin is (0, 0) and let us take 'p' as its horizontal semi axis and 'q' as its vertical semi axis, (x, y) are the coordinates, therefore the formula will be:

 x²       y²

---- + ----- = 1.

p²       q²

This is all about ellipse in maths.