Horizontal Hyperbola Formula
The horizontal hyperbola formula is used to represent the equation of a hyperbola that is oriented horizontally
The horizontal hyperbola formula is used to represent the equation of a hyperbola that is oriented horizontally. It is given by:
(x – h)² / a² – (y – k)² / b² = 1
Where (h, k) represents the center of the hyperbola, and a and b are the lengths of the horizontal and vertical axes, respectively.
The equation is written in standard form, where the constants a and b determine the shape and size of the hyperbola. The center (h, k) is the point where the transverse and conjugate axes intersect.
In this formula, the term (x – h)² determines the position of the horizontal branches of the hyperbola. The term (y – k)² determines the position and size of the vertical branches of the hyperbola.
To graph a horizontal hyperbola using this formula, we can follow these general steps:
1. Determine the center (h, k) of the hyperbola. It can be obtained from the given equation or given in the problem.
2. Calculate a and b, which represent the lengths of the horizontal and vertical axes, respectively. These can be obtained from the denominators of the equation.
3. Once you have the center and the lengths of the axes, you can plot the center on a graph. This point is the point of symmetry of the hyperbola.
4. Use the values of a and b to determine and mark the vertices, foci, and asymptotes of the hyperbola. The vertices can be found by moving a units to the left and right of the center along the x-axis. The foci can be found by moving c units from the center, where c is calculated using the formula c = √(a² + b²). The asymptotes can be found using the formula y = ± (b / a) * (x – h) + k.
5. Sketch the hyperbola, making sure the branches are symmetric with respect to the center. The hyperbola will have two disconnected, curved branches that open towards the right and left along the x-axis.
By using the horizontal hyperbola formula and following the steps mentioned above, you can graph a horizontal hyperbola with accuracy.
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