A circle touches the y -axis at the point (0, | vedclass

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Question

Equation of family of circle touching y-axis at $(0,4)$ is given by $(x-0)^{2}+(y-4)^{2}+\lambda x=0$

It passes through $(2,0)$ $\Rightarrow \quad

Vedclass · Accepted Answer

$4 x+3 y-8=0$

Vedclass · Answer

Equation of family of circle touching y-axis at $(0,4)$ is given by $(x-0)^{2}+(y-4)^{2}+\lambda x=0$

It passes through $(2,0)$ $\Rightarrow \quad \lambda=-10$

$\Rightarrow \quad$ Required circle is $(x-0)^{2}+(y-4)^{2}-10 x=0$

$\Rightarrow \quad x^{2}+y^{2}-10 x-8 y+16=0$

center of circle $\equiv(5,4)$ and radius $=5$ distance of $4 \mathrm{x}+3 \mathrm{y}-8=0$ from $(5,4)$

$=\left|\frac{24}{5}ight| 
eq$ radius

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?

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