Question 1185816
.
Center at (2,-2) vertex at (7,-2) and focus (4,-2) find the equation of the ellipse
~~~~~~~~~~~~~~~~~~


<pre>
(1)  Notice that the center and the vertex (and the focus) all lie on horizontal line y = -2.


     It means that the major axis is horizontal, and the major semi-axis is horizontal, too.

     
(2)  The length of the major semi-axis  " a "  is the distance between the vertex and the center, 
     i.e. equals 7-2 = 5 units:  a = 5.


(3)  The focal distance (between the center and the focus) is  4-2 = 2 units:  c = 2.


     Hence, for the minor semi-axis  "b"  we have  b = {{{sqrt(5^2 + 2^2)}}} = {{{sqrt(29)}}}.


(4) Thus the standard form equation of the ellipse is 


         {{{(x-2)^2/5^2}}} + {{{(y-(-2))^2/29}}} = 1,

     or

         {{{(x-2)^2/25}}} + {{{(y+2)^2/29}}} = 1.      <U>ANSWER</U>
</pre>

Solved.