9x^2+54x-y^2+10y+46=0 Find the center vertices foci and assymptotes

Question

Find the center foci vertices assymptotes for this Hyperbola.

Answer 1

The hyperbola equation is

To change the expressions (x² + 6x) and (y² - 10y) into a perfect square trinomial 

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

Standard form of horizontal hyperabola is

a is the number in denominator of the positive term.

If the x term is positive then the hyperbola is horizontal.

a = semi-transverse axis.

b = semi-conjugate axis.

Center

c = distance from the center to each focus along the transverse axis.

The equations for the asymptotes are

The equations for the asymptotes are