
# 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)

12.2E: The Hyperbola (Exercises) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.