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anonymous

  • one year ago

How would I solve this?

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  1. anonymous
    • one year ago
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  2. Jhannybean
    • one year ago
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    \[\large \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2} \longrightarrow \frac{(x-(-4))^2}{3^2} -\frac{(y-(-3))^2}{4^2}=1\]

  3. Jhannybean
    • one year ago
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    On the left you have the equation of a hyperbola, and the right arrow is what the equation of the hyperbola translates into, which is your function

  4. Jhannybean
    • one year ago
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    To find the foci and vertices, we need to identify what the center is. center : \((h,k)\)

  5. anonymous
    • one year ago
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    That's wrong, sorry.

  6. anonymous
    • one year ago
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    hmm

  7. Jhannybean
    • one year ago
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    ?...

  8. anonymous
    • one year ago
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    -4,-3

  9. Jhannybean
    • one year ago
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    Good.

  10. Jhannybean
    • one year ago
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    Now the foci lie along the horizontal transverse axis, what you know as the major axis. Therefore to find their location, we use the formula \[(h+c),k ~,~ (h-c),k~~, c^2=a^2+b^2 \longrightarrow c=\sqrt{a^2+b^2}\]

  11. anonymous
    • one year ago
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    c=5

  12. anonymous
    • one year ago
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    (1, -3,) (-9,-3)

  13. Jhannybean
    • one year ago
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    To find the vertices, you use the equation \[{(h+a),k} ~,~ {(h-a),k}\]

  14. anonymous
    • one year ago
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    (-1, -3) (-7,-3)

  15. anonymous
    • one year ago
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    ?

  16. Jhannybean
    • one year ago
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    Yes, c = 5. You are right.

  17. anonymous
    • one year ago
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    Thank you, could you help me with one more?

  18. Jhannybean
    • one year ago
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    Sure, i can try

  19. anonymous
    • one year ago
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    Thanks :) This is like the opposite I guess.

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  20. anonymous
    • one year ago
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    @Jhannybean

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spraguer (Moderator)
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