SOLUTION: Given 9 x²-4y²+18x+56y-223=0 Name the conic section, and how would you know?

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Question 752196: Given 9 x²-4y²+18x+56y-223=0
Name the conic section, and how would you know?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Given 9 x²-4y²+18x+56y-223=0
Name the conic section, and how would you know?
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9x²-4y²+18x+56y-223=0
complete the square
9x²+18x-4y²+56y-223=0
9(x²+2x+1)-4(y²+14y+49)=223+9-196
9(x+1)^2-4(y+7)^2=36
(x+1)^2/4-(y+7)^2/9=1
This conic is a hyperbola with horizontal transverse axis with center at (-1,-7)
Its standard form of equation: %28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1, (h,k)=(x,y) coordinates of center