Finding the equations of the lines and tangent to the circle

analytic-geometry

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 $\sqrt{3}y=2-x$.


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

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