12.2E: The Hyperbola (Exercises)
For the following exercises, write the equation of the hyperbola in standard form. Then give the center, vertices, and foci.
12. \(\frac{x^{2}}{81}-\frac{y^{2}}{9}=1\)
13. \(\frac{(y+1)^{2}}{16}-\frac{(x-4)^{2}}{36}=1\)
14. \(9 y^{2}-4 x^{2}+54 y-16 x+29=0\)
15. \(3 x^{2}-y^{2}-12 x-6 y-9=0\)
For the following exercises, graph the hyperbola, labeling vertices and foci.
16. \(\frac{x^{2}}{9}-\frac{y^{2}}{16}=1\)
17. \(\frac{(y-1)^{2}}{49}-\frac{(x+1)^{2}}{4}=1\)
18. \(x^{2}-4 y^{2}+6 x+32 y-91=0\)
19. \(2 y^{2}-x^{2}-12 y-6=0\)
For the following exercises, find the equation of the hyperbola.
20. Center at (0,0) , vertex at (0,4) , focus at (0,-6)
21. Foci at (3,7) and (7,7) , vertex at (6,7)