Question

Which conic section does this equation represent?

-4x^2-9x+4y^2+8x=16
A. Circle
B. Ellipse
C. Parabola
D. Hyperbola

Answer 1

-4x^2-9x+8x+4y^2=16
-4x^2-x+4y^2=16
-x^2-1x/4+y^2=4
-{x^2+x/4+(1/8)^2-(1/8)^2}+y^2=4
-(x+1/8)^2+1/64+y^2=4
-(x+1/8)^2+y^2=4-1/64=255/64
y^2/(255/64)-(x+1/8)^2/(255/64)=1
which is of the form y^2/a^2-x^2/b^2=1
which is a hyperbola.