please help!
2007-09-17 05:34:15 · 17 answers · asked by sand_illusions 4 in Science & Mathematics ➔ Mathematics
True. All circles are ellipses. They are merely special cases of ellipses.
However, not all ellipses are circles.
2007-09-17 06:19:53 · answer #1 · answered by Tina R 4 · 2⤊ 0⤋
True; a circle is a special case of an ellipse with zero eccentricity.
In an ellipse, the sum of the distances from any point on the ellipse to the two foci is a constant (which is always the length of the major axis of the ellipse).
In a circle, there is only one focus, the center of the circle, and all the points of the circle are equidistant from it. (This can be viewed a special case of the above, with a circle being an ellipse with two foci at the same point; the sum of the distances is the diameter.)
Therefore, all circles are ellipses, but not all ellipses are circles!
2007-09-17 12:49:47 · answer #2 · answered by Anthony P - Greece 2 · 2⤊ 0⤋
True. Circles are ellipses with eccentricity of 0, however then all ellipses are not circles because an ellipse can have an eccentricity anywhere between 0<=e<1 whereas a circle is defined by e=0.
2007-09-17 12:42:10 · answer #3 · answered by Anonymous · 2⤊ 0⤋
True. A circle is a special case of an ellipse with an eccentricity of 0.
Doug
2007-09-17 12:43:24 · answer #4 · answered by doug_donaghue 7 · 2⤊ 0⤋
An ellipse is the set of all points whose sum of distances from the two foci are equal.
Obviously this is true of a circle where the foci coincide at the center.
2007-09-18 08:55:04 · answer #5 · answered by Anonymous · 0⤊ 0⤋
True. Circles are ellipses with the major and minor axes are equal and the two focii coincide
2007-09-17 12:41:54 · answer #6 · answered by Pandian p.c. 3 · 3⤊ 0⤋
True.
Circles are merely special cases of ellipses where the two foci happen to be at exactly the same point.
2007-09-17 12:39:14 · answer #7 · answered by Mathsorcerer 7 · 4⤊ 0⤋
circle is a special case of ellipses,when major axis length =minor axis length...
we can say that all circles are ellipses
2007-09-17 12:40:31 · answer #8 · answered by msg_me 2 · 2⤊ 0⤋
True. I agree with most of the answers
Ana
2007-09-17 22:49:04 · answer #9 · answered by MathTutor 6 · 1⤊ 0⤋
True in the same respect that all squares are also rectangles.
2007-09-17 12:53:37 · answer #10 · answered by Emissary 6 · 2⤊ 0⤋