Question 552468: what is the focus of this conic section
9x^2+25y^2-200y+175=0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! what is the focus of this conic section
9x^2+25y^2-200y+175=0
complete the square
9x^2+25(y^2-8y+16)=-175+400
9x^2+25(y-4)^2=225
x^2/25+(y-4)^2/9=1
This is an equation of an ellipse with horizontal major axis of the standard form:
(x-h)^2/a^2+(y-k)^2/b^2=1, a>b, (h,k) being the (x,y) coordinates of the center.
For given equation:
Center: (0,4)
a^2=25
b^2=9
c^2=a^2-b^2=25-9=16
c=√16=4
Foci: (0±c,4)=(0±4,4)=(-4,4) and (4,4)
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