It is given that the sum of the distances from the point (3,0) and (9,0) is 12.
Let the point be (x, y)
Distance between the point of intersection & centre
Squaring both the sides,
x2 + 12x + 36 = 4x2 - 24x + 36 + 4y + 2
3x2 - 36x + 4y2=0
Hence, the required equation is 3x2 - 36x + 4y2 = 0.