Question

a disc of radius r in x-y plane with its centre at origin. The movement of a inertia of a disc about z-axis is equal to moment of inertia y=x+c.

Answer 1

As it is not clear what you meant, I take the mass of the disc m and radius r. Please change accordingly. The moment of inertia about z-axis.
mr22
The moment of inertia about p-axis.
mr24
I send a pic

Now,
d=csin450=c2
Using parallel axis theorem the MoI about p'-axis,
=mr24+md2=mr24+mc22
So,
mr22=mr24+mc22⇒mc22=mr24⇒c2=r22⇒c=r2