|
Question 74533This question is from textbook Algebra 2
: Hi! I just submitted this problem, but I think I figured it out! Can someone tell me if this is correct?
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.
The equation for an ellipse is y^2/a^2 + x^2/b^2=1.
So the answer would be y^2/36 + x^2/16=1.
Can someone please tell me if I did this right?
This question is from textbook Algebra 2
Found 2 solutions by stanbon, funmath:
Answer by stanbon(75887)   (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.
The equation for an ellipse is y^2/a^2 + x^2/b^2=1.
So the answer would be y^2/36 + x^2/16=1.
Can someone please tell me if I did this right?
---------------
Your equation would cause the center to be at (0,0)
If you plot the end points of the major and the minor axis you will
see that the center is at (1,0).
---------
Can you adjust your equation for that?
-------------
Cheers,
Stan H.
Answer by funmath(2933) (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.
You're right up to here, but this ellipse is not centered at the origin (0,0).
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:
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)
Happy Calculating!!!!
|
|
|
| |
