Question 625489: 16x^2 + 25y^2 - 96x - 200y + 144 = 0
find the center, foci, and vertices
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 16x^2 + 25y^2 - 96x - 200y + 144 = 0
find the center, foci, and vertices
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16x^2 + 25y^2 - 96x - 200y + 144 = 0
complete the squares:
16(x^2-6x+9)+25(y^2-8y+16)=-144+144+400
16(x-3)^2+25(y-4)^2=400
(x-3)^2/25+(y-4)^2/16=1
This is an equation of an ellipse with horizontal major axis.
Its standard form of equation: (x-h)^2/a^2+(y-k)^2/b^2=1, a>b, (h,k)=(x,y) coordinates of the center.
For given ellipse:
center: (3,4)
a^2=25
a=√25=5
vertices: (3±a,4)=(3±5,4)=(-2,4) and (8,4)
..
b^2=16
b=4
..
c^2=a^2-b^2=25-16=9
c=√9=3
Foci: (3±c,4)=(3±3,4)=(0,4) and (6,4)
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