filmov
tv
Given a point and both vertices, find the standard form of the hyperbola
Показать описание
Learn how to write the equation of hyperbolas given the characteristics of the hyperbolas. The standard form of the equation of a hyperbola is of the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2 / b^2 = 1 for vertical hyperbola.
The center of the hyperbola is given by (h, k). It is halfway between the two vertices and halfway between the two foci. 'a' is the distance from the center to the vertices and 'b' is the distance from the center to the covertices. 'c' is the distance from the center to the foci. The relationship between a, b and c is a^2 + b^2 = c^2. Using these characteristics of the hyperbola, we can then plug them into the standard equation to obtain the equation of the given hyperbola. When either 'a' or 'b' is unknown and a point on the hyperbola is known, then the point is plugged in into the equation of the hyperbola and the unknown value is solved for.
Note that a hyperbola is vertical when it is facing up and down and is horizontal when it is facing right and left. When a hyperbola is vertical, the vertices and the foci are in the y-axis but they are in the x-axis when the hyperbola is horizontal.
#conicsections #hyperbolaconicsections
#conicsections #hyperbolaconicsections
#conicsections #hyperbolaconicsections
The center of the hyperbola is given by (h, k). It is halfway between the two vertices and halfway between the two foci. 'a' is the distance from the center to the vertices and 'b' is the distance from the center to the covertices. 'c' is the distance from the center to the foci. The relationship between a, b and c is a^2 + b^2 = c^2. Using these characteristics of the hyperbola, we can then plug them into the standard equation to obtain the equation of the given hyperbola. When either 'a' or 'b' is unknown and a point on the hyperbola is known, then the point is plugged in into the equation of the hyperbola and the unknown value is solved for.
Note that a hyperbola is vertical when it is facing up and down and is horizontal when it is facing right and left. When a hyperbola is vertical, the vertices and the foci are in the y-axis but they are in the x-axis when the hyperbola is horizontal.
#conicsections #hyperbolaconicsections
#conicsections #hyperbolaconicsections
#conicsections #hyperbolaconicsections
0:06:33
Given a point and both vertices, find the standard form of the hyperbola
0:02:45
Given the midpoint and coordinates of point A, to find the coordinates of point B
0:04:37
Write the equation of a line given a slope and a point the line runs through
0:04:15
Graphing a Line Given Point and Slope │Linear Equations
0:07:37
How To Find The Equation of a Plane Given a Point and Perpendicular Normal Vector
0:12:50
Writing Linear Equations Given Two Points In Standard Form & Point Slope Form
0:02:26
Find Equation of Line Perpendicular to a Line Through a Given Point
0:02:25
How to find quadratic equation if turning point is given?
0:03:43
Writing an equation using point slope form given two points
0:04:12
How to Find the Slope of a Line Given Two Point? @MathTeacherGon
0:02:11
Graphing a line given point and slope | Linear equations & graphs | Algebra I | Khan Academy
0:02:16
Find the Equation of the Plane Given a Point and Normal Vector
0:08:28
Finding the Equation of a Line Given Slope and a Point - Point - Slope Form
0:00:55
Graphing a Line Through a Given Point with a Given Slope
0:03:36
Given a polar point find different ways to write the same point
0:02:49
How to determine another point on a graph given two points and the equation
0:05:28
Determining the quadratic equation given a vertex and a point
0:03:32
Given the point (1, 2), find theequation of a line on which it lies. How many such equations are...
0:05:06
Writing an equation using point slope form given two points
0:02:37
Writing an equation using point slope form given two points
0:01:58
Graphing a line through a given point with a given slope
0:02:58
Writing an equation using Point Slope form given two points
0:04:56
Write the equation of a parabola given a vertex and point
0:04:14
Finding the Equation of the Line given a point perpendicular to two points
Комментарии