What is Ellipse Formula?
Standard form of the equation of an ellipse centered at the origin is:
x2/a2 + y2/b2 = 1
If the ellipse is centered at (h, k), the equation becomes:
(x – h)2/a2 + (y – k)2/b2 = 1
where:
- a is the length of the semi-major axis (horizontal radius)
- b is the length of the semi-minor axis (vertical radius)
Now the ellipse formula is,
Take a point P at one end of the major axis. Total of the distances between point P and the foci is,
F1P + F2P = F1O + OP + F2P = c + a + (a–c) = 2a
Then, select a point Q on one end of the minor axis. The sum of the distances between Q and the foci is now,
F1Q + F2Q = √ (b2 + c2) + √ (b2 + c2) = 2√ (b2 + c2)
We already know that points P and Q are on the ellipse. As a result, by definition, we have
2√ (b2 + c2) = 2a
then √ (b2 + c2) = a
i.e. a2 = b2 + c2 or c2 = a2 – b2
The following is the equation for ellipse.
c2= a2 – b2
Ellipse Formula
An ellipse is a set of points such that the sum of the distances from any point on the ellipse to two fixed points (foci) is constant. In this article, we will learn about, Ellipse definition, Ellipse formulas and others in detail.
Table of Content
- What is Ellipse?
- What is Ellipse Formula?
- Major and Minor Axes Formula of Ellipse
- Eccentricity Formula of Ellipse
- Latus Rectum Formula of Ellipse
- Area of Ellipse Formula
- Perimeter of Ellipse Formula
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