Question 541810: To find coordinates, equation, and graph the ellipse with: center: (0,1) co-vertex: (0,6) major axis: 20 units long.
Vertices:
co-vertices:
Foci:
equation:
Can you help?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! To find coordinates, equation, and graph the ellipse with: center: (0,1) co-vertex: (0,6) major axis: 20 units long.
Vertices:
co-vertices:
Foci:
equation:
**
Standard form of equation for ellipse with horizontal major axis:
(x-h)^2/a^2+(y-k)^2/b^2=1,a>b, (h,k)=(x,y) coordinates of center
For given ellipse:
Center: (0,1)
length of minor axis=2*(6-1)=2*5=10
b=5
b^2=25
co-vertices: (0,1±b)=(0,1±5)=(0,-4) and (0,6)
..
length of major axis=20=2a
a=10
a^2=100
vertices: (0±a,1)=(0±10,1)=(-10,1) and (10,1)
..
c^2=a^2-b^2=100-25=75
c=√75
Foci:(0±c,1)=(0±√75,1)=(-√75,1) and (√75,1)
..
Equation of given ellipse:
(x-h)^2/a^2+(y-k)^2/b^2=1
(x-0)^2/100+(y-1)^2/25=1
x^2/100+(y-1)^2/25=1
see graph below as a visual check on answers above
..
y=±(25-x^2/4)^.5+1
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