ellipse

Problem 01 - Equation of a curve

Problem 01
Determine the equation of the curve such that the sum of the distances of any point of the curve from two points whose coordinates are (–3, 0) and (3, 0) is always equal to 8.
 

ellipse-problem-01-locus-abc.gif

 

Elements of Ellipse

Elements of the ellipse are shown in the figure below.
 

Elements of ellipse

 

The Ellipse

Definition of Ellipse
Ellipse is the locus of point that moves such that the sum of its distances from two fixed points called the foci is constant. The constant sum is the length of the major axis, 2a.
 

Conic Sections

Definition
Conic sections can be defined as the locus of point that moves so that the ratio of its distance from a fixed point called the focus to its distance from a fixed line called the directrix is constant. The constant ratio is called the eccentricity of the conic.
 

50 - 52 Nearest distance from a given point to a given curve

Problem 50
Find the shortest distance from the point (4, 2) to the ellipse x2 + 3y2 = 12.

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