Question

Which conic section does this equation represent?
x⅟₂-4x-y⅟₂ +6y-9=5
a) Ellipse
b)parabola
c)circle
d) hyperbola
I am thinking that it is D but I am not sure about it

Answer 1

If you mean
\(x^2-y^2-4x+6y-9=5\)
which is equivalent to
\((x-2)^2-(y+3)^2=27\)
It is a hyperbola centred at (2,-3) with a horizontal axis.