Who can tell me how to find the foci of a ellipse?

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 :)

In a circle, is the center the same as the focus?

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.

What do the pink dotted lines, which are connected to focus(foci), indicate?

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.

Is it necessary(in standard form) that the major or minor axis has to be the horizontal or vertical axis also?

no, they do not, but they do have to be parallel to the coordinate axis

How can we prove that the sum of squares of the reciprocals of two perpendicular diameters of an ellipse is constant?

I suspect what he means is how can we prove what is discussed (and proved) in the video "Foci of an ellipse from equation".

how do you make an equation when their are 2 foci?

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

Main content

Precalculus

Course: Precalculus > Unit 5

Lesson 2: Center and radii of an ellipse

Ellipse features review

Google Classroom

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 start color #1fab54, start text, m, a, j, o, r, space, r, a, d, i, u, s, end text, end color #1fab54 is longer than the start color #aa87ff, start text, m, i, n, o, r, space, r, a, d, i, u, s, end text, end color #aa87ff. In our example, the major radius is the horizontal one, but that could be otherwise.

The start color #1fab54, start text, m, a, j, o, r, space, a, x, i, s, end text, end color #1fab54 connects the ellipse's start color #1fab54, start text, v, e, r, t, i, c, e, s, end text, end color #1fab54, and the start color #aa87ff, start text, m, i, n, o, r, space, a, x, i, s, end text, end color #aa87ff connects the ellipse's start color #aa87ff, start text, c, o, negative, v, e, r, t, i, c, e, s, end text, end color #aa87ff. The axes are twice the size of their corresponding radii.

The start color #11accd, start text, c, e, n, t, e, r, end text, end color #11accd of the ellipse lies at the midpoint of its start color #1fab54, start text, v, e, r, t, i, c, e, s, end text, end color #1fab54, which is also the midpoint of its start color #aa87ff, start text, c, o, negative, v, e, r, t, i, c, e, s, end text, end color #aa87ff.

The start color #ed5fa6, start text, f, o, c, i, end text, end color #ed5fa6 of the ellipse lie on the start color #1fab54, start text, m, a, j, o, r, space, r, a, d, i, u, s, end text, end color #1fab54. 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.

Check your understanding

Problem 1

Current

What is the center of the ellipse?

(Choice A)
left parenthesis, 0, comma, 0, right parenthesis
(Choice B)
left parenthesis, minus, 2, comma, 0, right parenthesis
(Choice C)
left parenthesis, 0, comma, minus, 2, right parenthesis
(Choice D)
left parenthesis, 0, comma, minus, 3, right parenthesis

Want to try more problems like this? Check out this exercise.

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John He
Posted 6 years ago. Direct link to John He's post “Who can tell me how to fi...”
Who can tell me how to find the foci of a ellipse?
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(24 votes)
Answer
- Vanessa Borbe
  Posted 6 years ago. Direct link to Vanessa Borbe's post “c^2 = a^2 - b^2 is the fo...”
  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 :)
  Comment on Vanessa Borbe's post “c^2 = a^2 - b^2 is the fo...”
  (25 votes)
alexa.pomerantz
Posted 6 years ago. Direct link to alexa.pomerantz's post “In a circle, is the cente...”
In a circle, is the center the same as the focus?
Button navigates to signup pageComment on alexa.pomerantz's post “In a circle, is the cente...”
(4 votes)
Answer
- singh.dp.287
  Posted 5 years ago. Direct link to singh.dp.287's post “Basically Circle is a spe...”
  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.
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  (6 votes)
Akira
Posted 2 years ago. Direct link to Akira's post “What do the pink dotted l...”
What do the pink dotted lines, which are connected to focus(foci), indicate?
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(3 votes)
Answer
- Hecretary Bird
  Posted 2 years ago. Direct link to Hecretary Bird's post “The pink lines are basic...”
  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.
  Button navigates to signup page
  (5 votes)
Muhammad Amaanullah
Posted 5 years ago. Direct link to Muhammad Amaanullah's post “Is it necessary(in standa...”
Is it necessary(in standard form) that the major or minor axis has to be the horizontal or vertical axis also?
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(3 votes)
Answer
- Kevin S.
  Posted 4 years ago. Direct link to Kevin S.'s post “no, they do not, but they...”
  no, they do not, but they do have to be parallel to the coordinate axis
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  (3 votes)
VINAYAK AGARWAL
Posted 6 years ago. Direct link to VINAYAK AGARWAL's post “How can we prove that the...”
How can we prove that the sum of squares of the reciprocals of two perpendicular diameters of an ellipse is constant?
Button navigates to signup pageComment on VINAYAK AGARWAL's post “How can we prove that the...”
(0 votes)
Answer
- jma
  Posted 6 years ago. Direct link to jma's post “I suspect what he means i...”
  I suspect what he means is how can we prove what is discussed (and proved) in the video "Foci of an ellipse from equation".
  Comment on jma's post “I suspect what he means i...”
  (7 votes)
kaurjas
Posted 2 years ago. Direct link to kaurjas's post “how do you make an equati...”
how do you make an equation when their are 2 foci?
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(0 votes)
Answer
- loumast17
  Posted 2 years ago. Direct link to loumast17's post “https://www.khanacademy.o...”
  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
  Comment on loumast17's post “https://www.khanacademy.o...”
  (3 votes)
syed abuzar
Posted 6 years ago. Direct link to syed abuzar's post “If 2 line equations are g...”
If 2 line equations are given how to find tangent of ellipsie
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(0 votes)
Answer
- grey.gregory
  Posted 5 years ago. Direct link to grey.gregory's post “y−nx−m=s⟺y−ns(x−m)=1 (sou...”
  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.
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  (1 vote)