Miscellaneous

Is a set of all points in the plane the difference of whose distances from two fixed points?

by Author

Is a set of all points in the plane the difference of whose distances from two fixed points?

A hyperbola is the set of all points in a plane, the difference of whose distances from two fixed points (the foci) in the plane is a positive constant. The points where the hyperbola intersects the line joining the foci are the vertices. The vertices are a units from the center.

Is the set of all points in a plane the difference of whose distance between two fixed points F1 and F2 is a constant?

A hyperbola is the set of all points in the plane, the difference of whose distances from two fixed points F1 and F2 is a constant. These two fixed points are the foci of the hyperbola. The segment joining the two vertices on the separate branches is the transverse axis of the hyperbola.

READ:   Which processor is best for daily use laptop?

What figure is created by all points that are the same total distance from two points?

A circle is “the set of all points in a plane equidistant from a fixed point (center)”. The standard form for a circle, with center at the origin is x2 + y2 = r2, where r is the radius of the circle.

Is a set of all points in a plane the sum of whose distance?

An ellipse is the set of all points (x,y) in a plane such that the sum of their distances from two fixed points is a constant. Each fixed point is called a focus (plural: foci).

Is the set of all points?

Definition: A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. The a line segment from the center of the circle to any point on the circle is a radius of the circle.

What is the distance between Directrix of hyperbola?

READ:   Why is speaking Spanish important for globalization?

Distance between directrices = 2a / e. ∵ The eccentricity of rectangular hyperbola = √2.

How do you find the distance between two foci of a hyperbola?

A General Note: Standard Forms of the Equation of a Hyperbola with Center (h, k)

  1. the length of the transverse axis is 2a.
  2. the coordinates of the vertices are (h±a,k)
  3. the length of the conjugate axis is 2b.
  4. the coordinates of the co-vertices are (h,k±b)
  5. the distance between the foci is 2c , where c2=a2+b2.

How the distance formula and the Pythagorean theorem are related?

Derived from the Pythagorean Theorem, the distance formula is used to find the distance between two points in the plane. The Pythagorean Theorem, a2+b2=c2 a 2 + b 2 = c 2 , is based on a right triangle where a and b are the lengths of the legs adjacent to the right angle, and c is the length of the hypotenuse.

Is the set of all points in a plane?

Definition: A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. We use the symbol ⊙ to represent a circle. The a line segment from the center of the circle to any point on the circle is a radius of the circle. An arc is a connected portion of a circle.

READ:   How do you tell if a guy is only interested in hooking up?

Is the set of all points XY in a plane?

Unlike two-dimensional space, which consists of a single plane, the xy-plane, three-dimensional space contains infinitely many planes, just as two-dimensional space consists of infinitely many lines. Alternatively, the xy-plane can be described as the set of all points (x, y, z) for which z = 0.