# What Is an Ellipse

If you don't know what is an ellipse you should imagine a wheel (e.g. bike wheel). It is blown off evenly.

Look at the picture!

The wheel is unusable now but on the other hand we have a perfect ellipse. Our life helps us to know math!

So, what is an ellipse in math? An ellipse is a geometric figure. You can get it in the geometric plane.

Here is the canonical equation of the ellipse:

^{2}a

^{2}

^{2}b

^{2}

## Points:

O(0;0) | - | the centre of the ellipse |

A_{1}(-a;0) | - the tops of the ellipse | |

A_{2}(a;0) | ||

B_{1}(0;b) | ||

B_{2}(0;-b) | ||

|A_{1}A_{2}| = 2a | - | the major axis of the ellipse |

|B_{1}B_{2}| = 2b | - | the minor axis of the ellipse |

|OA_{1}| = |OA_{2}| = a | - | the semimajor axis of the ellipse |

|OB_{1}| = |OB_{2}| = b | - | the semiminor axis of the ellipse |

So, the canonical equation of the ellipse with the centre (0;0) and the semimajor axis a, the semiminor axis b is:

^{2}a

^{2}

^{2}b

^{2}

If you need an ellipse with the centre in the point K(x_{o};y_{o}), then you should use the equation:

_{o})

^{2}a

^{2}

_{o})

^{2}b

^{2}

|KA_{1}| = |KA_{2}| = a - the semimajor axis of the ellipse

|KB_{1}| = |KB_{2}| = b - the semiminor axis of the ellipse