prove that the line 2x + y = 1 is a tangent to the circle `x^2+y^2+6x-4y+8=0`.

Explanation

`x^2+y^2+6x-4y+8=0`
`therefore` g = 3, f = -2, c = 8
`therefore` Centre at (-3, 2) and radius is
sqrt(g^2+f^2-c) = sqrt(9+4-8) = sqrt5`
Distance of the centre from the line
2x + y -1 = 0 is `abs((2(-3)+1xx2-1)/sqrt(4+1))`
= `abs((-6+2-1)/sqrt5) = sqrt5`
`therefore` The line touches the circle`