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That's a circle. The "fixed point" is the center of the circle,

and the constant distance is its radius.

Q: A collection of points in the plane whose distance from fixed point is constant?

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It is the locus of points such that the sum of their distance from two distinct fixed points is a constant.

It is the locus of a point such that the sum of its distance from two (distinct) fixed points is a constant. So, given two fixed points, F1 and F2, an ellipse is the locus of the point P such that PF1 + PF2 is a constant. That would be an ellipsoid, a 3 dimensional thing. The 2 distances have to be measured in a fixed (2 dimensional) plane.

A half of a hyperbola is defined as the locus of points such that the distance of the point from one fixed point (a focus) and its distance from a fixed line (the directrix) is a constant that is greater than 1 (the eccentricity). By symmetry, a hyperbola has two foci and two directrices.

Basically a circle has a constant radius throughout and an ellipse does not.a circle has a constant radiusan ellipse has two foci. they are at either end of the ellipse

A circle is the locus of a point which moves such that its distance from a fixed point is constant. .The fixed point is centre and fixed distance is radius of circle. Elements of circle are centre, radius and circumference.

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It is the locus of points such that the sum of their distance from two distinct fixed points is a constant.

The center of the circle. That's how the circle is defined. (The collection of all points on a plane equidistant from a fixed point. The fixed point is the center and the fixed distance is the radius.)

I assume that you are asking about the definition of a circle. A circle is a locus of points in a plane that are at a constant distance from a fixed point.

It is the locus of a point such that the sum of its distance from two (distinct) fixed points is a constant. So, given two fixed points, F1 and F2, an ellipse is the locus of the point P such that PF1 + PF2 is a constant. That would be an ellipsoid, a 3 dimensional thing. The 2 distances have to be measured in a fixed (2 dimensional) plane.

A half of a hyperbola is defined as the locus of points such that the distance of the point from one fixed point (a focus) and its distance from a fixed line (the directrix) is a constant that is greater than 1 (the eccentricity). By symmetry, a hyperbola has two foci and two directrices.

Basically a circle has a constant radius throughout and an ellipse does not.a circle has a constant radiusan ellipse has two foci. they are at either end of the ellipse

The simple answer is that an ellipse is a squashed circle.A more precise answer is that an ellipse is the locus (a collection) of points such that the sum of their distances from two fixed points (called foci) remains a constant. A circle is the locus of points that are all the same distance from a fixed point. If the two foci are moved closer together, the ellipse becomes more and more like a circle and finally, when they coincide, the ellipse becomes a circle. So, a circle is a special case of an ellipse.

an ellipse.

A circle is the locus of a point which moves such that its distance from a fixed point is constant. .The fixed point is centre and fixed distance is radius of circle. Elements of circle are centre, radius and circumference.

CIRCLE

triangle

It is the locus of all points such that their distance from a fixed line (the directrix) is the same as their distance from a fixed point which is not on that line (the focus).