Question 591913: write an equation in vertex form then graph it. Label center,verticies,co-verticies and the foci> x^2+4y^2=16
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! write an equation in vertex form then graph it. Label center,verticies,co-verticies and the foci> x^2+4y^2=16
divide by 16
x^2/16+y^2/4=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)=(x,y) coordinates of center.
For given ellipse:
center:(0,0)
a^2=16
a=√16=4
vertices: (0±a,0)=(0±4,0)=(-4,0) and (4,0)
..
b^2=4
b=√4=2
co-vertices: (0,0±b)= (0,0±2)=(0,-2) and (0,2)
..
c^2=a^2-b^2=16-4=12
c=√12≈3.46
Foci:(0±c,0)=(0±√12,0)=(-3.46,0) and (3.46,0)
see graph below:
y=±(4-x^2/4)^.5
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