(c) Since circle touches x -axis at (3,0) ∴ The equation of circle be (x−3)2+(y−0)2+λy=0
As it passes through (1,-2) ∴ Put x=1,y=−2 ⇒(1−3)2+(−2)2+λ(−2)=0 ⇒λ=4 ∴ equation of circle is (x−3)2+y2−8=0 Now, from the options (5,-2) satisfies equation of circle.