SOLUTION: find th eequation of ellipse having the given point as foci and the given number as the sum of the focal radi (-9,0)(9,0);30

Let  "a"  and  "b"  be the major and minor semi-axes of the ellipse, respectively.


Then from the condition you have these two equations


(1)   (9+a) + (a-9) = 30             ( <<<---=== "the sum of the focal radii = 30" )
                                     ( it is the sum of the distances from foci to the vertex of the ellipse !)

      which becomes  2a = 30  ====>  a = 15.



(2)    = 9            ( <<<---=== the distance from the center of the ellipse to its focus is 9).


      Then (2) implies   =  =  = 144,

      hence,  b =  = 12.



Thus the semi-axes are 15 and 12 units long,  and the equation of the ellipse is

 +  = 1.