f.5 equation of circle

1)
circle C touches the y-axis at (0,3) and it intersects the x-axis at (1,0),
find the equation of circle.
ans: x^2+y^2-10x-6y+9=0

2)If the straight line 3x-2y+38=0 is the tangent to the circle
x^2+y^2+4x-6y+c=0, find the value of c.
ans: -39

3)It is given that the circle x^2+y^2+2x+6y-30=0 and the straight line x-2y-3=0 intersect at P and Q.Find the equation of circle that passes through P and Q with the smallest radius.
ans: 5x^2+5y^2+14x+22y-162=0