1. The problem statement, all variables and given/known data Find the equation of the tangent drawn from the point(-5,4) to the circle x^2+y^2-2x-4y+1=0 2. Relevant equations y-y1=m(x-x1) x^2+y^2+2gx+2fy+c=0 3. The attempt at a solution The equation of the tangent using the point is as follows y-4=m(x+5). Now, if I substitute the value of y in the given equation of the circle the equation gets messy as there will be two variables m and x in the quadratic equation. Is there any elegant way to solve the slope of the tangent line without having to go through the trouble of substituting the value of y into the given equation of the circle..