A circle touches the$y-$axis at the point ($0,4$) and passes through the point ($(2,0)$ . Which of the following lines is not a tangent to this circle?

Equation of a circle touching y-axis at  $(0,4)\text{ is }(x-0{)}^2+(y-4{)}^2+\lambda x=0$

$\Rightarrow x^2+y^2+\lambda x-8y+16=0$

If this circle passes through $(2,0)\text{ then }4+0+2\lambda -0+16=0\Rightarrow 2\lambda =-20\Rightarrow \lambda =-10$

$\therefore$ Equation of the circle touching y-axis at $(0,4)$  and passing through $(2,0)$ is 

$x^2+y^2-10x-8y+16=0$

Now centre of the circle  $C=(5,4)$ radius of the circle $r=\sqrt{25+16-16}=5$

Distance from $C$ to $3x+4y-6=0$ is $\left|\frac{15+16-6}{\sqrt{9+16}}\right|=\frac{25}{5}=5=r$

Distance from  $C$ to $3x-4y-24=0\text{ is }\left|\frac{15-16-24}{\sqrt{9+16}}\right|=\frac{25}{5}=5=r$

Distance from $C$ to $4x-3y+17=0\text{ is }\left|\frac{20-12+17}{\sqrt{16+9}}\right|=\frac{25}{5}=5=r$

Distance from $C$  to $4x+3y-8=0\text{ is }\left|\frac{20+12-8}{\sqrt{16+9}}\right|=\frac{24}{5}\ne r$