Hyperbolas: Asymptotes and Equations
Master hyperbola orientation, standard forms, asymptote formulas, and key relationships.
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Questions Covered in This Set
10 cards to master
What is the standard form of a horizontal hyperbola centered at the origin?
$$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$
What is the standard form of a vertical hyperbola centered at the origin?
$$\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$$
How do you determine if a hyperbola is horizontal or vertical?
The positive term indicates the transverse axis: positive x² means horizontal, positive y² means vertical.
What are the asymptotes of a horizontal hyperbola $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$?
$$y = \pm \frac{b}{a}x$$
What are the asymptotes of a vertical hyperbola $$\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$$?
$$y = \pm \frac{a}{b}x$$
What is the relationship between a, b, and c in a hyperbola?
$$c^2 = a^2 + b^2$$, where c is the distance from center to each focus.
Where are the vertices of a horizontal hyperbola centered at the origin?
$$(\pm a, 0)$$
Where are the foci of a vertical hyperbola centered at (h, k)?
$$(h, k \pm c)$$ where $$c = \sqrt{a^2 + b^2}$$
What is the asymptote formula for a vertical hyperbola centered at (h, k)?
$$y - k = \pm \frac{a}{b}(x - h)$$
What trick helps you find asymptotes from the standard form?
Replace the 1 with 0 in the equation and solve for y in terms of x.
