A hyperbola's orientation can be determined by its standard equation. If the equation is in the form ((y-k)^2/a^2 - (x-h)^2/b^2 = 1), the hyperbola opens vertically, while if it is in the form ((x-h)^2/a^2 - (y-k)^2/b^2 = 1), it opens horizontally. The center ((h, k)) is the midpoint between the vertices, which also helps in visualizing the hyperbola's direction. Additionally, the placement of the squared terms indicates the direction of the branches.
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If a hyperbola is vertical, the asymptotes have a slope of m = +- a/b. If a hyperbola is horizontal, the asymptotes have a slope of m = +- b/a.
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there is only one way i know how to find the slope of a hyperbola and that is taking the implicit derivative of its equation, and solving for dy/dx but the answer is Slope= (x)*(b^2) / (y)*(a^2)
Asymptotes are the guidelines that a hyperbola follows. They form an X and the hyperbola always gets closer to them but never touches them. If the transverse axis of your hyperbola is horizontal, the slopes of your asymptotes are + or - b/a. If the transverse axis is vertical, the slopes are + or - a/b. The center of a hyperbola is (h,k). I don't know what the rest of your questions are, though.
Defn: A hyperbola is said to be a rectangular hyperbola if its asymptotes are at right angles. Std Eqn: The standard rectangular hyperbola xy = c2
Two foci's are found on a hyperbola graph.
If a hyperbola is vertical, the asymptotes have a slope of m = +- a/b. If a hyperbola is horizontal, the asymptotes have a slope of m = +- b/a.
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The axes of the hyperbola.
find the constant difference for a hyperbola with foci f1 (5,0) and f2(5,0) and the point on the hyperbola (1,0).