Official solution
Equation of family of circle touching y-axis at
(0, 4) is given by (x -- 0)2 + (y -- 4)2 + \[\lambda \]x = 0.
\[ \because \] It passes through (2, 0)
\[ \Rightarrow \] \[\lambda \] = --10.
\[ \Rightarrow \] Required circle is (x -- 0)2 + (y -- 4)2 -- 10x = 0
\[ \Rightarrow \] x2 + y2 -- 10x -- 8y + 16 = 0
\[ \therefore \] center of circle (5, 4) and radius = 5
By checking all options you can see 4x + 3y -- 8 = 0 is not a tangent to the circle.
As distance of 4x + 3y -- 8 = 0 from (5, 4)
= \[\left| {{{24} \over 5}} \right|\] \[ \ne \] radius