Prove that the line \(y=mx+c\) will touch the circle \(x^2+y^2=25\) if \(c^2=25(1+m^2)\).

The blue circle here is \(x^2 + y^2 = 25,\) while the green line is \(y = mx + c\).

When a line and a circle touch, what can we say about their equations?

Hence or otherwise find the equations of the two tangents to this circle from the point \((2,11)\).

What else can we write down about \(c\) and \(m\) if we know a point on the line?