Consider the equation of ellipse, 4x2+9y2−24x+36y=0 Then 4(x2−6x+9)+9(y2+4y+5)−36−36‌‌=0 4(x−3)2+9(y+2)2‌‌=72 ‌
(x−3)2
18
+‌
(y+2)2
8
‌‌=1 Here required locus is director circle so, (x−3)2+(y+2)2‌‌=26 x2−6x+9+y2+4+4y‌‌=26 x2+y2−6x+4y‌‌=13 x2+y2−6x+4y−13‌‌=0