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About Ellipses

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About Ellipses, a selection of answers from the Dr. Math archives.

Ellipse & Parabola Formulas - Dr. Math FAQ
A conic (or conic section) is a plane curve that can be obtained by intersecting a cone with a plane that does not go through the vertex of the cone... If no line of the cone is parallel to the plane, the intersection is a closed curve, called an ellipse.

Uses of Ellipses
Where are ellipses found in real life?

Difference between Oval and Ellipse
What is the difference between an oval and an ellipse? Am I right if I say that "all ellipses are ovals, but all ovals cannot be ellipses"?

Perimeter of an Oval
What is the perimeter of an oval called?

Drawing an Ellipse

Drawing An Ellipse
How do you draw an ellipse with only a straight edge and a compass?

Accurate Drawing of an Ellipse
Draw an ellipse accurately using simple tools.

Tracing an Ellipse
How do you form an ellipse using 3 points?

Area

Ellipse Area and Circumference
How can I draw an ellipse and find the area and circumference?

Area of an Oval
How do I figure out the area of an oval 17" x 38"?

Area of an Ellipse using Integral Calculus
How do you find the area of an ellipse?

Area of an Ellipse without using Calculus
How do you find the area of an oval without using calculus?

Area of Part of an Ellipse
Given an ellipse with a line bisecting it perpendicular to either the major or minor axis of the ellipse, what is the formula for the area of the ellipse either above or below that line?

Area of an Ellipse Cut by a Chord
How can you calculate area of the part of an ellipse cut off by a chord, if you know the major and minor axes, and the chord?

Area of A Sector of An Ellipse
Finding the area of a sector of an ellipse, given the semiminor and major axes and the angles of the 2 vectors bounding the sector.

Perimeter

Circumference of an Ellipse
Is there a formula for determining the circumference or distance around an ellipse?

Formula for the Circumference of an Ellipse
What is the formula for the circumference of an ellipse?

The Perimeter of an Ellipse or Oval
What is the formula for calculating the perimeter of an oval, or an ellipse?

Perimeter of an Ellipse
Is there a formula that gives the exact perimeter of an ellipse?

Equations, Graphing...

Foci of an Ellipse
If the major and minor axis of an ellipse are given, how do I find the focus points?

Graphing an Ellipse
How do you graph an ellipse? What is the equation?

Definition of an Ellipse
The equation for an ellipse is Pf + Pr= 2a where P is a point on the ellipse and f and r are the points of the foci. How do we know that this is true, that Pf + Pr = 2a? How did we come up with the constant of 2a?

Distance from Point to Ellipse
How do you find the minimum distance from a point to an ellipse when the point can be either inside or outside the ellipse?

Ellipse Equation
How do I get the equation of an ellipse, given four points and the inclination of the major axis?

Point on an Ellipse
Given an ellipse and an arbitrary angle theta from either axis, how do you find the coordinates of the intersection of the ellipse and a vector formed by angle theta?

Points within an Ellipse
How to generate points that will be within an ellipse.

Folding a Circle to Get an Ellipse
How can I prove that taking a point on a circle, folding it to an interior point, and repeating this process creates an envelope of folds that forms an ellipse?

Ellipse Geometry
I wish to draw a line departing at a given angle from the long axis of an ellipse and bisecting the perimeter of the ellipse at right angles to the tangent at that point...

Tangent Common to Two Ellipses
I have two general ellipses in space and I want to find the equation of the tangent common to these ellipses.

Slope of Tangent to an Ellipse
If I know a point on an ellipse, how do I find the angle of the ellipse at that point?

Finding the Axes of an Ellipse from a Known Cone
I'm trying to solve a specific situation regarding lighting when viewed as an oblique circular cone...

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High School Conic Sections/Circles
Index of Selected Answers to Common Questions

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