Obtain the equation of the circle orthogonal to both the circles `x^2+y^2+3x-5y+6=0` and `4x^@+4y^2-28x+29=0` and whose centre lies on the line `3x+4y+1=0`

Find the equation to the circle orthogonal to the two circles x^(2)+y^(2)-4x6y+11=0;x^(2)+y^(2)-10x-4y+21=0 and has 2x+3y=7 as diameter.

Find the equation of the circle which touches the lines 4x-3y+10=0 and 4x-3y-30=0 and whose centre lies on the line 2x+y=0 .

Find the equation of radical axis of the circles x^(2)+y^(2)-3x+5y-7=0 and 2x^(2)+2y^(2)-4x+8y-13=0 .

Find the equations of the two circles which intersect the circles x^2+y^2-6y+1=0 and x^2+y^2-4y+1=0 orthogonally and touch the line 3x+4y+5=0

Find the equation of the circle through the points of interrection of the circles x^(2)+y^(2)-4x-6y-12=0 and x^(2)+y^(2)+6x+4y-12=0 and cutting the circle x^(2)+y^(2)-2x-4=0 orthogonally.