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What figure is the locus of all points such that the sum of the distances from the point to two fixed points is 6 cm?
The locus of all points such that the sum of the distances from the point to two fixed points is a constant (in this case, 6 cm) is an ellipse. The two fixed points are called the foci of the ellipse. The total distance of 6 cm is the major axis length of the ellipse, indicating that the foci are separated by a distance less than 6 cm, ensuring that the ellipse is defined.
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What figure is the locus of all points such that the sum of the distances from the point to two points is 6cm?
http://en.wikipedia.org/wiki/Elipse
What figure is the locus of all points that are equidistant from two fixed points?
A line in 2D and a plane in 3D A perpendicular bisector of the line connecting the 2 given points
What is the definition of ellipse in math terms?
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.
Is it true that the locus of points idea can be used to define straight lines circles and even more complex shapes such as parabolas?
Yes, the locus of points concept can be used to define various geometric shapes. A straight line can be defined as the locus of points equidistant from two fixed points, while a circle is the locus of points equidistant from a single fixed point (the center). More complex shapes, such as parabolas, can also be defined as loci; for instance, a parabola can be described as the locus of points equidistant from a fixed point (the focus) and a fixed line (the directrix).
What is the locus of points in a plane that are equidistant from two fixed points?
I believe that is the definition of a straight line.
What figure is the locus of all points such that the sum of the distances from the point to two points is 6cm?
http://en.wikipedia.org/wiki/Elipse
What figure is the locus of all points that are equidistant from two fixed points?
A line in 2D and a plane in 3D A perpendicular bisector of the line connecting the 2 given points
What is the definition of ellipse in math terms?
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.
Is it true that the locus of points idea can be used to define straight lines circles and even more complex shapes such as parabolas?
Yes, the locus of points concept can be used to define various geometric shapes. A straight line can be defined as the locus of points equidistant from two fixed points, while a circle is the locus of points equidistant from a single fixed point (the center). More complex shapes, such as parabolas, can also be defined as loci; for instance, a parabola can be described as the locus of points equidistant from a fixed point (the focus) and a fixed line (the directrix).
The locus of points idea allows you to define objects in terms of points and given distances?
true
What is the locus of all points that are a fixed distance from a given point?
triangle
What is the locus of points in a plane that are equidistant from two fixed points?
I believe that is the definition of a straight line.
Which of these is the best definition for ellipse?
It is the locus of points such that the sum of their distance from two distinct fixed points is a constant.
A compass draws all points that are equidistant from a fixed point thereby creating a locus of points for a circle?
A circle is the locus of all points equidistant from a given point, which is the center of the circle, and a circle can be drawn with a compass. (The phrase "locus of points for a circle" does not seem to be conventionally defined.) or true
A compass draws all points a given distance from a fixed point thereby creating a locus of points for a circle?
True
A compass draws all points at a uniform distance from a fixed point thereby creating a locus of points for a circle?
true
The locus of points idea can be used to define straight lines circles and even more complex shapes as parabolas?
The locus of points refers to the set of all points that satisfy a given condition or equation. For straight lines, the locus can be defined by a linear equation, while circles are defined as the set of points equidistant from a center point. Parabolas, on the other hand, can be described as the locus of points equidistant from a fixed point (the focus) and a fixed line (the directrix). This concept allows for the geometric representation of various shapes based on specific conditions.
