Question 674682
<pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi
x^2 + y^2 - 4x + 2y = 15
x^2 - 4x + 4 + y^2 + 2y + 1 = 15 + 4 + 1
{{{(x-2)^2 + (y+1)^2 = 20}}}  C(2,-1)  r = sqrt(20) = 2sqrt(5)
 C(2,-1)
  (4,-5)  m = 4/-2 = -2
tangent Line  m = 1/2
 y = (1/2)x + b   ||Using the  (x,y) ordered pair (4,-5) to solve for b
-5 =(1/2)4 + b
-7 = b
 y = (1/2)x -7
{{{drawing(300,300,   -6, 6, -6, 6,  grid(1),
circle(2, -1,0.2),
circle(2, -1,2sqrt(5)),
circle(4,-5,0.2),
graph( 300, 300, -6, 6, -6, 6,0, .5x-7))}}}