Finding the equations of the lines and tangent to the circle

Question

Find the equations of the lines through $(2,0)$ and tangent to the circle $x^2+y^2=1$. I tried to solve this and I know the right answer but I just can't solve this. The right answer: $\sqrt{3}y=x-2$ or $\sqrt{3}y=2-x$.

Answer 1

HINT:

The equation of any line passing through $(2,0)$ can be written as $$\frac{y-0}{x-2}=m\iff y=m(x-2)$$ where $m$ is the gradient or slope

Now replace the value of $y$ in $x^2+y^2=1$ to form a Quadratic Equation in $x$

For tangency, the roots of the equation must be same i..e, the discriminant must be zero

Answer 2

HINT:

The equation of any line passing through $(2,0)$ can be written as $$\frac{y-0}{x-2}=m\iff mx-y-2m=0\ \ \ \ (1)$$ where $m$ is the gradient or slope

From this, the distance of a tangent from the center of the respective circle equals to the radius

Now can you calculate the distance of $(1)$ from the center$(0,0)$?