Circles Part 1

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