Question 688211
How do I put the equation in standard form? The vertices and the center of the equation are also needed: 
-16x^2 - 4y^2 = 48x - 20y + 57
-16x^2 - 4y^2 = 48x - 20y + 57
16x^2+48x+4y^2-20y=-57
complete the square
16(x^2+3x+9/4)+4(y^2-5y+25/4=-57+36+25
16(x+3/2)^2+4(y+5/2)^2=4
{{{4(x+3/2)^2+(y-5/2)^2=1}}}
This is an equation of an ellipse with vertical major axis.
Its standard form:{{{(x-h)^2/b^2+(y-k)^2/a^2=1}}},a>b, (h,k)=(x,y) coordinates of center
center: (-3/2,5/2)
a^2=1
a=1
vertices=(-3/2,5/2±a)=(-3/2,5/2±1)=(-3/2,3/2) and (-3/2,7/2)