Locus of centres of the circles which touch the two circles `x^2 + y^2 = 16` and `x^2 + y^2 = 16x` externally is

For the two circles: x^2+y^2 =16 and x^2+y^2-2y =0 there :

The locus of the centre of the circle which moves such that it touches the circle (x + 1)^(2) + y^(2) = 1 externally and also the y-axis is

The locus of the centre of the circle which moves such that it touches the circle (x + 1)^(2) + y^(2) = 1 externally and also the y-axis is

The locus of the centre of a circle which touches externally the circle x^(2)+y^(2)=a^(2) and x^(2)+y^(2)=4ax externally has the equation.

For the two circles x^(2) + y^(2) =16 and x^(2) + y^(2) -2y =0 there is/are

The locus of centres of all circles which touch the line x = 2a and cut the circle x^2 + y^2 = a^2 orthogonally is

The locus of centres of all circles which touch the line x = 2a and cut the circle x^2 + y^2 = a^2 orthogonally is