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## Precalculus

### Course: Precalculus > Unit 5

Lesson 2: Center and radii of an ellipse# Ellipse features review

Review all the features of an ellipse: center, vertices, co-vertices, major radius, minor radius, and foci.

## What are the features of an ellipse?

An ellipse has two radii of unequal size: the ${\text{major radius}}$ is longer than the ${\text{minor radius}}$ . In our example, the major radius is the horizontal one, but that could be otherwise.

The ${\text{major axis}}$ connects the ellipse's ${\text{vertices}}$ , and the ${\text{minor axis}}$ connects the ellipse's ${\text{co-vertices}}$ . The axes are twice the size of their corresponding radii.

The ${\text{center}}$ of the ellipse lies at the midpoint of its ${\text{vertices}}$ , which is also the midpoint of its ${\text{co-vertices}}$ .

The ${\text{foci}}$ of the ellipse lie on the ${\text{major radius}}$ . Their special property is that the sum of the distances from the foci to each point on the ellipse is always the same.

*Want to learn more about ellipses? Check out this video.*

## Want to join the conversation?

- Who can tell me how to find the foci of a ellipse?(27 votes)
- c^2 = a^2 - b^2 is the focal distance. The foci is basically *(c,0)(-c,0) or (0,c)(0,-c)*. It depends on whether your ellipse is vertical or horizontal.

To make it easier, I first get 'a,b and c', given an equation. From there, I get the coordinates of the vertex, co-vertex, foci and the measure of the major axis (2a), minor axis (2b), and focal length (c^2). It makes it easier for me :)(28 votes)

- In a circle, is the center the same as the focus?(4 votes)
- Basically Circle is a special case of ellipse just as a square is a special case of rectangle.In a circle both the minor and major radii are the same. Also the foci and centre coincide.(8 votes)

- What do the pink dotted lines, which are connected to focus(foci), indicate?(3 votes)
- The pink lines are basically a representation of how you get the ellipse in the first place. As the article says, the sum of the distances from the foci to any one point on the ellipse will always be constant. The pink lines are a possible set of distances from one point to the foci.

You can draw an ellipse using a pencil and string, by fixing both ends of the string at the foci and using the pencil to draw out the shape. The length of the string (the sum of the distances from the foci) will obviously be the same, which means that we end up drawing an ellipse. This is because the definition of an ellipse is the set of all points, the sum of whose distances from the 2 foci is constant.(6 votes)

- Is it necessary(in standard form) that the major or minor axis has to be the horizontal or vertical axis also?(3 votes)
- no, they do not, but they do have to be parallel to the coordinate axis(3 votes)

- How do this work?(1 vote)
- What do you mean? Please give a clear question so that i can help you(3 votes)

- If 2 line equations are given how to find tangent of ellipsie(1 vote)
- y−nx−m=s⟺y−ns(x−m)=1 (source: AmWhy. “Find the Equation of the Tangent Line to the Ellipse at the given Point.” Implicit Differentiation - Find the Equation of the Tangent Line to the Ellipse at the given Point - Mathematics Stack Exchange, Stack Exchange, Inc., 4 Oct. 2014.(2 votes)

- how do you make an equation when their are 2 foci?(0 votes)
- https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-foci/a/ellipse-foci-review

If you just have foci you can't make an exact equation, becuase multiple ellipse can have the same two foci(5 votes)

- How can we prove that the sum of squares of the reciprocals of two perpendicular diameters of an ellipse is constant?(0 votes)
- I suspect what he means is how can we prove what is discussed (and proved) in the video "Foci of an ellipse from equation".(7 votes)