Answer is (3) 4x + 3y – 8 = 0
Equation of family of circle touching y-axis at (0, 4) is given by (x – 0)2 + (y – 4)2 + λx = 0.
∵ It passes through (2, 0)
⇒ λ = –10.
⇒ Required circle is (x – 0)2 + (y – 4)2 – 10x = 0
⇒ x2 + y2 – 10x – 8y + 16 = 0
center of circle ≡ (5, 4) and radius = 5
distance of 4x + 3y – 8 = 0 from (5, 4)
= |24/5| ≠ radius