SOLUTION: Hi! Can someone please help me with this problem? Write an equation for an ellipse if the points of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis ar

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Hi! Can someone please help me with this problem? Write an equation for an ellipse if the points of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis ar      Log On


   

Question 74529This question is from textbook Algebra 2
: Hi! Can someone please help me with this problem?
Write an equation for an ellipse if the points of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0).

Thanks! This question is from textbook Algebra 2

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0).

The length of the major axis would be 12 units. 2a=12. a=6.
The length of the minor axis is 8 units. 2b=8. b=4.
Notice that the x coordinate of the end points of the major axis is 1.
The y coordinate of the end points of the minor axis is 0.
That means that the center is (1,0).
This can be seen if you draw your ellipse.
The formula for an ellipse with a vertical major axis is:
highlight%28%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1%29
major axis=2a
minor axis=2b
Center=(h,k)
You found that a=6 and b=4 and now you know that (h,k)=(1,0)
%28x-1%29%5E2%2F4%5E2%2B%28y-0%29%5E2%2F6%5E2=1
highlight%28%28x-1%29%5E2%2F16%2By%5E2%2F36=1%29
Happy Calculating!!!!