Hyperbolas in Standard Form

Practice Problems: Hyperbolas in Standard Form

1. 1. Which equation represents a hyperbola with a horizontal transverse axis?
2. 2. For the hyperbola $\frac{x^2}{25} - \frac{y^2}{16} = 1$, what is the value of $a$?
3. 3. What is the center of the hyperbola $\frac{(x-3)^2}{16} - \frac{(y+2)^2}{9} = 1$? Enter as $(h, k)$
4. 4. For a hyperbola with $a = 3$ and $b = 4$, what is $c$?
5. 5. What are the vertices of the hyperbola $\frac{x^2}{9} - \frac{y^2}{4} = 1$?
6. 6. What is the slope of the asymptotes for $\frac{x^2}{16} - \frac{y^2}{9} = 1$? Enter as a fraction.
7. 7. What are the foci of $\frac{x^2}{9} - \frac{y^2}{16} = 1$?
8. 8. Find the center, vertices, and foci of $\frac{(x+1)^2}{4} - \frac{(y-2)^2}{5} = 1$
9. 9. Write the standard form equation for a hyperbola with center $(0,0)$, vertex at $(0, 4)$, and focus at $(0, 5)$. Enter as y^2/a - x^2/b = 1
10. 10. What is the equation of the asymptotes for $\frac{(y-1)^2}{9} - \frac{(x+2)^2}{4} = 1$?
11. 11. Convert $9x^2 - 4y^2 - 36x - 8y - 4 = 0$ to standard form.
12. 12. A hyperbola has foci at $(-6, 0)$ and $(6, 0)$, and the difference of distances from any point on the hyperbola to the foci is 8. What is $a$?
13. 13. Write the equation of the hyperbola with foci at $(0, -5)$ and $(0, 5)$ passing through the point $(3, 4)$.
14. 14. The eccentricity $e = \frac{c}{a}$ of a hyperbola with $a^2 = 9$ and $b^2 = 16$ is:
15. 15. Find all key features of $\frac{(x-1)^2}{36} - \frac{(y+2)^2}{64} = 1$