Question 703148
Determine if the given equation describes ellipse, or hyperbola. Also write each in standard form.
x^2+9y^2-8x-90y+232=0
x^2-8x+9y^2-90y+232=0
x^2-8x+9y^2-90y=-232
complete the squares
(x^2-8x+16)+9(y^2-10y+25)=-232+16+225
(x-4)^2+9(y-5)^2=9
{{{(x-4)^2/9+(y-5)^2=1}}}
This is an equation of an ellipse with horizontal major axis and center at (4,5)
Its standard form: {{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}, a>b, (h,k)=(x,y) coordinates of center