SOLUTION: 9x^2-16y^2+36x+64y=172 What type of conic? Standard Form?

Question 241372: 9x^2-16y^2+36x+64y=172

What type of conic?
Standard Form?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
9x^2-16y^2+36x+64y=172
What type of conic?
Standard Form?
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Since the squared terms have opposite signs
the conic is a hyperbola.
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Form:
Complete the square on the x and on the y terms:
9(x^2 + 4x) - 16(y^2-4y) = 172
Complete the two squares:
9(x^2 + 4x + 4) - 16(y^2 - 4y + 4) = 172 + 9*4 -16*4
9(x+2)^2 - 16(y-2)^2 = 144
Divide thru by 144 to get:
(x+2)^2/16 - (y-2)^2/9 = 1
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Cheers,
Stan H.
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