Question 975428
ven the ellipse: 9x2 + 4y2 + 18x - 48y + 117 = 0 
a) Put the equation in standard form 
b) Horizontal or vertical major axis? 
c) Find center, vertices, foci, 
length of major and minor axes, 
and eccentricity 
d)	Sketch a graph of this ellipse.
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9x^2+18x+4y^2-48y=-117
complete the square:
9(x^2+2x+1)+4(y^2-12y+36)=-117+9+144
9(x+1)^2+4(y-6)^2=36
a){{{(x+1)^2/4+(y-6)^2/9=1}}}
b)this is an equation of an ellipse with vertical major axis
its standard form of equation: {{{(x-h)^2/b^2+(y-k)^2/a^2=1}}}, a>b, (h,k)=coordinates of c)center
center: (-1, 6)
a^2=9
a=3
length of major axis=2a=6
vertices: (-1, 6±a)=(-1, 6±3)=(-1, 3) and (-1, 9)
b^2=4
b=2
length of minor axis=2b=4
c^2=a^2-b^2=9-4=5
c=√5≈2.2
foci:  (-1, 6±c)=(-1, 6±2.2)=(-1, 3.8) and (-1, 8.2)
d)see graph below:
y=((36-9(x+1)^2)/4)^.5+6
{{{ graph( 300, 300, -10, 10, -10, 10,((36-9(x+1)^2)/4)^.5+6,-((36-9(x+1)^2)/4)^.5+6) }}}