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Mathematics LibreTexts

12.2E: The Hyperbola (Exercises)

  • Page ID
    56132
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    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.

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