Given that the equation of a circle is X & sup2; + Y & sup2; + 2x-8y + 8 = 0, the length of PA is an important process if P (2,0) is a tangent of the circle and the tangent point is a

Given that the equation of a circle is X & sup2; + Y & sup2; + 2x-8y + 8 = 0, the length of PA is an important process if P (2,0) is a tangent of the circle and the tangent point is a

The equation of circle is reduced to the standard equation (x + 1) &# 178; + (y-4) &# 178; = 9
So the far radius is 3, and the center of the circle is (- 1,4)
Let the center of a circle be o, then
OA=3,OP=√（2+1)²+4²=5
Because the triangle apo is a right triangle
So PA = √ OP & # 178; - OA & # 178; = 4

If the equation x ^ 2 + y ^ 2 + 2x-8y + 8 = 0 of a circle is known, and a tangent is made through the point P (2,0), then the length of the tangent is?

4