How do you identify the vertices, foci, and direction of #-10y-y^2=-4x^2-72x-199#?
Write the equation in one of the two standard forms then use information to find the vertices and foci.
Remove a common factor of 4 from the first 3 terms and a common factor of -1 from the next 3 terms:
Use the right side of the patterns
Substitute the left side of the patterns into equation :
Substitute the values for h and k into equation :
Simplify the right side of equation :
Divide both sides of the equation by 100:
Write the denominators as squares:
Equation  is the standard form for a hyperbola with a horizontal transverse axis.
Referring to the standard form, the vertices are at
The vertices are
Referring to the standard form, the foci are at
The foci are
Referring to the standard form, the asymptotes are at:
The asymptotes are: