Ellipse and its equation

Ellipse is twisted circle, it got major features and equation from circle.

Ellipse got TWO radiuses (or radii):

• Major radius: the longer one.
• Minor radius: the shorter one.

Standard ellipse equation

a, b is the radius on x-axis and y-axis. Ellipse originally centred at (0, 0).

Foci of ellipse

Since ellipse is part of Conic section, so it has the same identity:

There’re TWO points on the Major radius of ellipse, so that any point on this ellipse has the same sum of distance to both points. These two points are called Focuses or Foci.

How to find the Foci

• Major radius on X-axis: f² = a²-b²
• Major radius on Y-axis: f² = b²-a²

Foci identity

With the distance D₁ and D₂, their sum is equal to Double Major Radius:

D₁ + D₂ = 2*r