Question

Classify the conic section: 9x^2+16y^2-72x+64y+64=0
A.circle
B.Ellipse
C.Hyperbola
D.parabola

Answer 1

Looks like you might need to complete the square to help solve this....

Answer 2

That's my guess to help

Answer 3

horizontal ellipse :)
http://www.wolframalpha.com/input/?i=+9x%5E2%2B16y%5E2-72x%2B64y%2B64%3D0+
and yes you have to complete the square to figure this out:
\[ 9x^2+16y^2-72x+64y+64=0 \]\[9x^2-72x+16y^2+64y=-64\]\[9(x^2-8\color{blue}{+16})+16(y^2+4y\color{blue}{+4})=-64\color{blue}{+144+64}\]\[9(x-4)^2+16(y+2)^2=144\]\[{{9(x-4)^2}\over144}+{{16(y+2)^2}\over144}=1\]\[{(x-4)^2\over16}+{(y+2)^2\over9}=1\]and that is an equation of an ellipse, specifically, horizontal

Answer 4

Thank you!! that really helped me a lot! @yummydum @juanjohnguy

Answer 5

No problem even though yummydum did all the work lol