Given,
L1=4x−3y+K1=0;L2=4x−3y+K2=0
Here line L1 and L2 are parallel.
So,

Now point A(−1,2) will satisfy L1 so, −4−3×2+K2=0 ⇒K2=10
Also point B(3,−6) will satisfy L2=4x−3y+K2
So 4×3−3×(−6)+K2=0⇒K2=−30
Now distance between the parallel line will be the diameter
Diameter =∣42+32K1−K2∣
=∣510+30∣=8
So radius 28=4
Now mid-point of AB will give us centre of circle by symmetry, so by midpoint formula in AB we get centre (1,−2),
Now equation of circle will be (x−1)2+(y+2)2=42