Question 949013: Identify the center, vertices, co-vertices, foci, length of the major axis, length of the minor axis, and eccentricity of:
X squared + 9y squared + 8x + 108y +331= 0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Identify the center, vertices, co-vertices, foci, length of the major axis, length of the minor axis, and eccentricity of:
X squared + 9y squared + 8x + 108y +331= 0
***
x^2+9y^2+8x+108y+331=0
x^2+8x+9y^2+108y=-331
complete the square:
(x^2+8x+16)+9(y^2+12y+36)=-331+16+324
(x+4)^2+9(y+6)^2=9
This is an equation of an ellipse with horizontal major axis
Its standard form of equation: , a>b, (h,k)=coordinates of center
center: (-4,-6)
a^2=9
a=√9=3
length of major axis=2a=6
b^2=1
b=1
length of minor axis=2b=2
vertices: (-4±a,-6)=(-4±3,-6)=(-7,-6) and (-1,-6)
co-vertices: (-4-6±b)=(-4,-6±1)=(-4,-7) and (-4,-5)
..
c^2=a^2-b^2=9-1=8
c=√8≈2.8
foci: (-4±c,-6)=(-4±2.8,-6)=(-6.8,-6) and (-1.2,-6)
eccentricity=c/a=√8/3≈0.94
see graph below:
|
|
|
