Consider the conic section given by the equation $$144 y^2 - 1152 y - 25 x^2 + 100 x + 2204 = 3600$$ Which conic section is it? (Acceptable answers are: ellipse, hyperbola and parabola.)
Answer:
The first focus of this conic has coordinates (,). (Order the foci according to the order of their $x$ or $y$ coordinates, ie. $(-1,5)$ precedes $(3,5)$ and $(2,1)$ precedes $(2,4)$.)
The second focus of this conic has coordinates (,). (If the conic is a parabola, just repeat the coordinates of the first focus.)
The equation of the directrix is $=0$. (If the conic is a parabola, write the directrix in the form $x-p=0$ or $y-p=0$. If the conic is an ellipse or hyperbola, write the equation $1=0$, an impossible equation.)
The axis of the conic has equation $=0$. (The axis of a conic is the line joining the foci and the vertices. For an ellipse this is also known as the major axis. Write the equation in the form $x-c=0$ or $y-c=0$.)
The asymptote of positive slope has equation $y=$ . (If the conic is not a hyperbola put $y+1$ on the right hand side of the equation, giving an impossible equation.)
The asymptote of negative slope has equation $y=$ . (If the conic is not a hyperbola put $y+1$ on the right hand side of the equation, giving an impossible equation.)