SOLUTION: I have a problem with a graph. Here is the link. http://s194.photobucket.com/albums/z4/dbrine/?action=view&current=t6q12.jpg

Algebra ->  Trigonometry-basics -> SOLUTION: I have a problem with a graph. Here is the link. http://s194.photobucket.com/albums/z4/dbrine/?action=view&current=t6q12.jpg      Log On


   

Question 88883: I have a problem with a graph. Here is the link.
http://s194.photobucket.com/albums/z4/dbrine/?action=view¤t=t6q12.jpg
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the center:
Since the ellipse stretches from x=1 to x=9, this means the horizontal center is the average of 1 and 9. So add 1 and 9 and divide by 2

%281%2B9%29%2F2=10%2F2=5

So the horizontal center is x=5


Since the ellipse stretches from y=1 to x=7, this means the vertical center is the average of 1 and 7. So add 1 and 7 and divide by 2

%281%2B7%29%2F2=8%2F2=4

So the vertical center is y=4


So the center of the ellipse is (5,4)

----------------------------------------------------------------------------
Now lets find the radii:

Now we can find the horizontal radius by subtracting 5 from 9 (this will find the distance from the horizontal center to either the left or right edge)

9-5=4

So the horizontal radius is 4 (ie it is 4 units from the center to the edge if you use the x-axis)


We can find the vertical radius by subtracting 4 from 7 (this will find the distance from the vertical center to either the top or bottom edge)

7-4=3

So the vertical radius is 3 (ie it is 3 units from the center to the edge if you use the y-axis)


===============================================================================



Now using the general equation of the ellipse

%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1 where (h,k) is the center, a is the horizontal radius, and b is the vertical radius

%28x-5%29%5E2%2F4%5E2%2B%28y-4%29%5E2%2F3%5E2=1 Plug in h=5, k=4, a=4 and b=3 (these were solved for earlier)

%28x-5%29%5E2%2F16%2B%28y-4%29%5E2%2F9=1 Square each value


Notice if we graph the equation (you need to solve for y first) we get





and this shows that our answer is correct.


So the answer is B)