Question 975428: Given 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.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 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)
b)this is an equation of an ellipse with vertical major axis
its standard form of equation:  , 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
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