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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
9 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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