x^2-4y^2+8x-24y-24=0

Question

classify the conic section

Answer 1

The equation is

The conic section is a hyperbola since x²  and y²  have opposite signs.

To change the expressions (x ² + 8x) and (y ² + 6y) into a perfect square trinomial,

add (half the x coefficient)² and add (half the y coefficient)² to each side of the equation.

Divide each side by 4 .

Now it is in the form of horizontal hyperbola  .