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Show all steps to solve 9x^2-4y^2+54x+8y+78=0 and put in standard hyperbola form.?

This involves completing the square for both x and y but can't seem to get into the standard hyperbola form: (y-k)^2/a^2 -(x-h)^2/b^2 = 1

Update:

OK. I was able to complete the squares of both quadratics to get

9*(x+3)^2 - 4*(y-1)^2 = -78 + 81 - 4--multiplying thru by -1 gave me the vertical hyperbola but not in the correct form... That gave me 4*(y-1)^2 -9*(x+3)^2 = 1

if I divide every term by 36 I don't get 1 on the RHS...more help needed.

2 Answers

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  • 9 years ago
    Favorite Answer

    4(Y -1)² -9(X +3)² = 1

    you just need to think of a = 1/2 and b = 1/3 and you should be able to see that it is in the right form:

    (Y -1)²/(1/4) - (X +3)²/(1/9) = 1

    do you recognize it now?

    (Y -1)² / (1/2)² - (X +3)² / (1/3)² = 1

  • 4 years ago

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