Identifying Conic Sections help, please!

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Identifying Conic Sections help, please!

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Conic sections are the curves which can be derived from taking slices of a "double-napped" cone.
I understand all of it besides the last part, and I have -9(x-7)^2 + 16 (y-5)^2=144

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I know that I multiply (1/144) by each side but the (-9) is throwing me off.
its an hyperbola
But How do you get the final equation so you know it's a hyperbola?
-9 (x-14) x+16 (y-10) y-185 = 0
-9 (x-7)^2+16 (y-5)^2-144 = 0
So, the final equation we want looks like this: (x-h)^2/a^2-(y-k)^2/b^2=1 From your equation above, is the next step to divide 144?
yeah
OKay, this is where I get confused because wouldn't it be: -9/144(x-7)^2+16/144(y-5)^2=1
yes
did i help you?
Sorry my computer crashed. Ok so I'm getting an ellipse. (X+7)^2/16 + (y-5)^2/9=1
nope its an hyperbola
When you divide 144 to -9(x-7)^2 would your result be (x+7)^2/16 because the -1 makes x-7^2 a positive (x+7)^2
Never mind! I got it!! Thanks for your help! The equation would be: (y-50^2/9-(x-7)^2/16

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