Standard Equations for Ellipse

The ellipse equation with its center at the origin and its major axis along the x-axis is:

x2/a2+y2/b2 = 1

where –a ≤ x ≤ a.

The ellipse equation with the center at the origin and the major axis along the y-axis is:

x2/b2+y2/a2 = 1

where –b  ≤ y ≤ b.

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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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What is Ellipse?

In geometry, an ellipse is a two-dimensional shape described along its axes. When a cone is intersected by a plane at an angle with respect to its base, an ellipse is created. There are two focal points. The total of the two distances to the focal point is always constant for all places along the curve. A circle is also an ellipse in which the foci are all at the same location, which is the circle’s centre....

Definition

The locus of all the points on an XY-plane, whose sum of the distance from two fixed points is constant is called an Ellipse....

Ellipse Shape

In geometry, an ellipse is a two-dimensional shape, that is defined along its axes. An ellipse is formed when a cone is intersected by a plane at an angle with respect to its base....

Major and Minor Axis

An Ellipse has two axes along the x-axis and the y-axis that support its structure. They are called,...

Eccentricity of Ellipse

The eccentricity of an ellipse is defined as the ratio of distances from the centre of the ellipse to the semi-major axis of the ellipse....

Properties of Ellipse

Various properties of an ellipse are,...

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...

Derivation of Ellipse Equation

The figure represents an ellipse such that P1F1 + P1F2 = P2F1 + P2F2 = P3F1 + P3F2 is a constant. This constant is always greater than the distance between the two foci. When both the foci are joined with the help of a line segment then the mid-point of this line segment joining the foci is known as the centre....

Ellipse Formula

Ellipse is somewhat similar to a circle which is stretched along its diameter. It is a 2-D figure so its area and perimeter can easily be calculated....

Latus Rectum

Latus Rectum is defined as the line segments perpendicular to the major axis of the ellipse and passing through any of the foci in such a manner that their endpoints always lie on the ellipse....

Standard Equations for Ellipse

The ellipse equation with its center at the origin and its major axis along the x-axis is: x2/a2+y2/b2 = 1 where –a ≤ x ≤ a. The ellipse equation with the center at the origin and the major axis along the y-axis is: x2/b2+y2/a2 = 1 where –b  ≤ y ≤ b....

Solved Examples on Ellipse

Example 1: If the length of the semi-major axis is given as 10 cm and the semi-minor axis is 7 cm of an ellipse. Find its area....

FAQs on Ellipse

Question 1: What is an ellipse?...

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