which conic section is defined by 25x^2-50x-4y^2+24y=111 show work

Question

please help!

Answer 1

The equation is

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

To change the expressions (x ²- 2x) 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 100 .

Now it is in the form of horizontal hyperbola  .