Tangent lines to a circle through exterior point

Question

Hello,

I have an assignment where one of the questions is to find parametric equations for the tangent lines to a circle x^2 + y^2 = 1 which pass through (2, 0).

I have tried finding dy/dx via implicit differentiation, and  I get dy/dx = -x/y, which is not defined for (2, 0), right?

At this point I get stuck, and am not sure where to go, so any hints or insights would be helpful.

Thanks.

Answer 1

You might be overthinking this; unless you have been *told* to use calculus, this problem ought to yield to more elementary techniques.

Your first step should be to *find* the tangent lines. I suggest drawing a careful picture on some graph paper.

Answer 2

>I have tried finding dy/dx via implicit differentiation, and I get dy/dx = -x/y, which is not defined for (2, 0), right?

(2,0) is not a point on the circle, so it wouldn't make sense to use the derivative **of the circle** to calculate the slope at that point