|
Question 536231: Find an equation for the ellipse that satisfies the given conditions.
Foci (0, ±3), length of minor axis 8
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find an equation for the ellipse that satisfies the given conditions.
Foci (0, ±3), length of minor axis 8
**
Given coordinates of the Foci show this is an ellipse with vertical major axis (y-coordinates change while x-coordinates do not). Standard form of equation: (x-h)^2/b^2+(y-k)^2/a^2=1,
a>b, (h,k) being the (x,y) coordinates of the center.
For given ellipse:
x-coordinate of center=0 (given)
y-coordinate of center=mid point of Foci on vertical major axis=0
Center: (0,0)
..
length of minor axis=8 (given)=2b
b=4
b^2=16
..
c=3
c^2=a^2-b^2
a^2=c^2+b^2=9+16=25
..
Equation of ellipse:
(x-0)^2/16+(y-0)^2/25=1
x^2/16+y^2/25=1
|
|
|
| |
