Admin Table of Contents
- 1 How do you find the equation of a hyperbola given the transverse axis?
- 2 How do you find the length of the transverse axis of a hyperbola?
- 3 How do you write the equation of a hyperbola?
- 4 What is the general equation of hyperbola?
- 5 What is the standard form of the equation of a hyperbola?
- 6 What are the most important terms related to hyperbola?
How do you find the equation of a hyperbola given the transverse axis?
A hyperbola with a horizontal transverse axis and center at (h, k) has one asymptote with equation y = k + (x – h) and the other with equation y = k – (x – h). A hyperbola with a vertical transverse axis and center at (h, k) has one asymptote with equation y = k + (x – h) and the other with equation y = k – (x – h).
How do you find the length of the transverse axis of a hyperbola?
A General Note: Standard Forms of the Equation of a Hyperbola with Center (h, k)
- the length of the transverse axis is 2a.
- the coordinates of the vertices are (h±a,k)
- the length of the conjugate axis is 2b.
- the coordinates of the co-vertices are (h,k±b)
- the distance between the foci is 2c , where c2=a2+b2.
How do you write an equation for a hyperbola?
The equation of a hyperbola written in the form (y−k)2b2−(x−h)2a2=1. The center is (h,k), b defines the transverse axis, and a defines the conjugate axis. The line segment formed by the vertices of a hyperbola.
What is the transverse axis length?
This means the transverse axis is horizontal and the conjugate axis is vertical. The length of the transverse axis is the distance between the two vertices, which is 6.
How do you write the equation of a hyperbola?
What is the general equation of hyperbola?
STANDARD FORMS OF EQUATIONS OF CONIC SECTIONS:
| Circle | (x−h)2+(y−k)2=r2 |
|---|---|
| Hyperbola with horizontal transverse axis | (x−h)2a2−(y−k)2b2=1 |
| Hyperbola with vertical transverse axis | (y−k)2a2−(x−h)2b2=1 |
| Parabola with horizontal axis | (y−k)2=4p(x−h) , p≠0 |
| Parabola with vertical axis | (x−h)2=4p(y−k) , p≠0 |
Does the hyperbola have a horizontal transverse axis?
By the Midpoint Formula, the center of the hyperbola occurs at the point Furthermore, and and it follows that So, the hyperbola has a horizontal transverse axis and the standard form of the equation is See Figure 10.32. This equation simplifies to
How do you find the origin of a hyperbola?
The point at which the intercepts of hyperbola coincide with vertices, it is centered as an origin. If the equation is of the form x 2 / a 2 – y 2 / b 2 = 1, then the axis of the transverse line lies on the x-axis.
What is the standard form of the equation of a hyperbola?
The standard form of the equation of a hyperbolawith center is Transverse axis is horizontal. Transverse axis is vertical. The vertices are units from the center, and the foci are units from the center. Moreover, If the center of the hyperbola is at the origin the equation takes one of the following forms. Transverse axis is vertical. y2 a2 x2
Some of the most important terms related to hyperbola are: 1 Eccentricity (e): e 2 = 1 + (b 2 / a 2) = 1 + [ (conjugate axis) 2 / (transverse axis) 2] 2 Focii: S = (ae, 0) & S′ = (−ae, 0) 3 Directrix: x= (a/e), x = (−a / e) 4 Transverse axis: More