Ellipse Formula
Take a point P at one end of the major axis, as indicated. As a result, the 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
An ellipse is the locus of all points on a plane with constant distances from two fixed points in the plane. The fixed points encircled by the curve are known as foci (singular focus). The constant ratio is the eccentricity of the ellipse and the fixed line is the directrix. In this article, we will learn about the ellipse in detail.
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