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Which best describes a parabola?
Given a straight line (a directrix) and a point (the focus) which is not on that line, a parabola is locus of all points whose distance form the directrix is the same as its distance from the focus.
What is the locus of points that are 10 centimeters from a given point?
The locus of points (or collection of all points) that are 10 centimeters from a given point would be a circle (of radius 10 cm) in two dimensions, and a sphere (of radius 10 cm) in three dimensions.
Although the locus of points idea can be used to define a straight line and circle more complex shapes such as parabolas must be defined a different way. True or False?
Certainly false for parabolae; a parabola is the locus of points in a plane which are equidistant from a point (the focus) and a line (the directrix) in that plane. It's also false for an ellipse, which is the locus of points in a plane where the sum of the distances from two other points in that plane (the foci) is constant. AND false for a hyperbola, which is the locus of points in a plane where the absolute value of the DIFFERENCE in the distance from two points in that plane (also the foci) is constant. Alternatively, a hyperbola is the locus of points in a plane where the ratio of the distance to one of the foci and to a line (the directrix) is constant (which is larger than 1; if it's exactly equal to 1, you get a parabola instead).All of these are only slightly more complicated than circles, and in fact they, alone with circles, are called "conic sections" because they all are formed by the intersection of a plane with a right circular conical surface.
What best describes a single fixed point that is the same distance from the parabola as the directrix is from the parabola?
Locus
What is a radius of 1 cm?
It is the set of all points that are at a distance of 1 cm from a fixed point (called the centre).
What is the locus of points at a given distance from a given point?
A circle
What is a locus of points equidistant from a point?
A locus of points is just the set of points satisfying a given condition. The locus of points equidistant from a point is a circle, since a circle is just a set of points which are all the same distance away from the center
What is the locus of all points that are a fixed distance from a given point?
triangle
The locus of points that are the same distance from a point and a line is a .?
The locus of points that are the same distance from a point and a line is a parabola. In this scenario, the point acts as the focus of the parabola, while the line serves as the directrix. The shape of the parabola opens away from the line, with all points on the curve equidistant from both the focus and the directrix.
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
Is locus is center of circle or any point on circumference of circle?
The center isn't the locus, and a point on the circumference isn't the locus.The whole circumference of the circle is the locus.It's the locus of all points that have the same distance from the center of the circle.
Which is the locus of a point at which potential due to an isolated point charge is constant?
The locus of points where the potential due to an isolated point charge is constant is a spherical surface centered on the point charge. This is because the potential decreases with distance from the point charge, so points at the same distance will have the same potential.
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.
Is line is a locus of point?
No. A line is the locus of all points located between any two points.
Locus of points equidistant from a point?
circle
What does parabola mean in mathematical terms?
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).
