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The equation √[(x-2) 2 +(y-1) 2 ] + √[(x+2) 2 +(y-4) 2 ]=5 represents circle/ ellipse/ line segment??? Elaborate how.

The equation √[(x-2)2+(y-1)2]  + √[(x+2)2+(y-4)2]=5 represents circle/ ellipse/ line segment??? Elaborate how.

Grade:12th Pass

1 Answers

RAJORSHI PAUL
36 Points
10 years ago

The given eqn is the eqn of an ellipse.If you note carefully you will find that the eqn represents the sum of the distances of a point (x,y) from (2,1) & (-2,4) resp. which is constant & equal to 5. This basically is the definition of an ellipse. Ellipse is defined as a curve in which the sum of the distances of any point on it from the focii is constant.Here the focii of the ellipse are (2,1) & (-2,4).

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