General form of the circle : 2x^2 + 2y^2 -6x -10y -15 =0
So, standard form of the circle is
(x - 1.5)^2 + (y-2.5)^2 = 4^2
Therefore center lies in (3/2 , 5/2), So (I) is false.
Distance from center of circle to origin = sqrt( (1.5-0)^2 + (2.5-0)^2 ) = sqrt(8.5)
Since distance from center of circle to origin, sqrt(8.5) < radius of circle, 4
Therefore option (II) is true
Area of circle = pi * 4 * 4= 3.14 * 16 = 50.24 sq unit (approx)
Since 50.24 < 55, therefore option (III) is true