Question

Tangent to the x-axis ; center on 2x+y-1=0; radius 5.

Answer 1

tangent to the x -axis means the y-coordinate of the center is 5 (k =5)
center on 2x +y -1 =0 means the x-coordinate of the center (h) is on the line and (h,k) is satisfy the equation. In other word, 2h +k -1 =0 or 2h = 1-k =1-5 =-4
so, the equation of the circle is \((x+4)^2 +(y-5)^2=25\)