SOLUTION: Find the equation of an ellipse with its center at (1,2), focus at (6, 2) and containing the point (4,6). I have so far (x-1)^2 + (y-2)^2 = 1, but I cannot figure out what my

Since the center and focus have the same y-value, 
we know this is an ellipse whose major axis is 
horizontal, so its equation is in the form:



The center is (,)

The left focus is (,) and the 
right focus is (,), where 

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We substitute the center (h,k) = (1,2)



We substitute the given point (x,y) = (4,6)







The focus given (,) must be a right focus
since (,) is right of the center (,), so

(,) = (,) 
  
So  and of course and since 

   

     

Now using the fact that  substituting :





So we have this system of equations:





Can you solve that for  and  by substitution? 
If not post again asking how.

You get  and 

Substituting in 





Edwin