Horizontal Hyperbola Formula
The formula for a horizontal hyperbola can be represented as:
(x – h)^2 / a^2 – (y – k)^2 / b^2 = 1
where (h, k) represents the center of the hyperbola, a represents the distance from the center to the vertex in the x-direction, and b represents the distance from the center to the vertex in the y-direction
The formula for a horizontal hyperbola can be represented as:
(x – h)^2 / a^2 – (y – k)^2 / b^2 = 1
where (h, k) represents the center of the hyperbola, a represents the distance from the center to the vertex in the x-direction, and b represents the distance from the center to the vertex in the y-direction.
To graph a horizontal hyperbola, follow these steps:
Step 1: Identify the center of the hyperbola, which is the point (h, k) in the formula.
Step 2: Determine the values of a and b. The value of a is the distance from the center to the vertex in the x-direction, and b is the distance from the center to the vertex in the y-direction.
Step 3: Plot the center point (h, k) on the coordinate plane.
Step 4: Use the values of a, b, and the center point to plot the vertices. The vertices will be at the points (h + a, k) and (h – a, k).
Step 5: Calculate the values of c, which represents the distance from the center to the foci. The formula to find c is c = √(a^2 + b^2).
Step 6: Use the value of c to plot the foci on the coordinate plane. The foci will be at the points (h + c, k) and (h – c, k).
Step 7: Draw the asymptotes, which are straight lines passing through the center (h, k) and intersecting the vertices. The slope of the asymptotes can be found using the formula m = ±(b / a).
Step 8: Sketch the hyperbola by drawing the two branches using the vertices as reference points. The branches curve outward from the center and seem to approach the asymptotes.
Remember, the direction of the hyperbola (horizontal or vertical) depends on the sign in the equation. If the x term is positive (x – h)^2, then it is horizontal. If the y term is positive, it is vertical.
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