Find the equation of the circle which passes through (1,-2),(3,-4) and touches the X-axis.
Let the equation of the circle be
The circle touches x-axis means
It passes thro'(1,-2)
Let this equation be 1.
Required circle passes through (3,-4)
Let this equation be 2.
Solving the two equations,we get
The value of f is
Hence the equations of the circle are