The equation of the image of the circle x^2+y^2+16x-24y+183=0 by the line mirror 4x+7y+13=0 is

the line               4x+7y+13=0  will be same   

we will get one equation in terms of ( h , k) 

and the midpoint of ( h , k )  and ( - 8 , 12 )  will lie on the line 

will get another equation in ( h , k )

we can easily find out the values of k