SOLUTION: graph the ellipse given by (x-5)^2/81+(y-9)^2/25=1

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Question 698944: graph the ellipse given by (x-5)^2/81+(y-9)^2/25=1
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Ellipses like this drawing%2820%2C10%2C-2%2C2%2C-1%2C1%2Carc%280%2C0%2C-3.9%2C1.9%29+%29 have equations of this form with aČ under the term in x 

%28x-h%29%5E2%2Fa%5E2%22%22%2B%22%22%28y-k%29%5E2%2Fb%5E2%22%22=%22%221

Ellipses like this drawing%2810%2C20%2C-1%2C1%2C-2%2C2%2Carc%280%2C0%2C1.9%2C-3.9%29+%29 have equations of this form with aČ under the term in y 

%28x-h%29%5E2%2Fb%5E2%22%22%2B%22%22%28y-k%29%5E2%2Fa%5E2%22%22=%22%221

a is always greater than b, and of course aČ is greater than bČ.

%28x-h%29%5E2%2Fb%5E2%22%22%2B%22%22%28y-k%29%5E2%2Fa%5E2%22%22=%22%221

The center is (h,k), the semi-major axis is a, the semi minor axis is b.

%28x-5%29%5E2%2F81%22%22%2B%22%22%28y-9%29%5E2%2F25%22%22=%22%221

Since the denominator 81 is larger than the denominator 25, so we know
this is an ellipse that looks like this drawing%2820%2C10%2C-2%2C2%2C-1%2C1%2Carc%280%2C0%2C-3.9%2C1.9%29+%29 

By comparison h=5, k=9, aČ=81, bČ=25, and so a=9, b=5

So the center is (h,k) = (5,9). The major axis is 2a=18, and the minor
axis is 2b=10, and the two axes bisect each other at the center (5,9), 
so we draw this:



Edwin