Question 614894: Which two endpoints define the major axis 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! Which two endpoints define the major axis of this conic section?
9x^2 + 25y^2 - 200y + 175=0
complete the square:
25(y^2-8y+16)+9x^2=-175+400
25(y-4)^2+9x^2=225
x^2/25+(y-4)^2/9=1
This is an equation of an ellipse with horizontal major axis.
Its standard form: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), (h,k)=(x,y) coordinates of center
For given equation:x^2/25+(y-4)^2/9=1
center:(0,4)
a^2=25
a=√25=5
vertices (endpoints of horizontal major axis):
(0±a,4)=(0±5,4)=(-5,4) and (5,4)
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