Question 88883
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


{{{(1+9)/2=10/2=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


{{{(1+7)/2=8/2=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 


{{{(x-h)^2/a^2+(y-k)^2/b^2=1}}} where (h,k) is the center, a is the horizontal radius, and  b is the vertical radius


{{{(x-5)^2/4^2+(y-4)^2/3^2=1}}} Plug in {{{h=5}}}, {{{k=4}}}, {{{a=4}}} and {{{b=3}}} (these were solved for earlier)


{{{(x-5)^2/16+(y-4)^2/9=1}}} Square each value



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




{{{drawing( 500, 500, -10, 10, -10, 10, 
grid(1),
graph( 500, 500, -10, 10, -10, 10, sqrt(9(1-(x-5)^2/16))+4, -sqrt(9(1-(x-5)^2/16))+4)

)}}}


and this shows that our answer is correct.



So the answer is B)