Locus and nine point circle

If origin is the orthocentre of the triangle formed by the points (5,-1),(-2,3) and (-4,-7) then the nine point circle centre

Orthocentre of the triangle is (2,1) and the circumcentre is ((7)/(2),(5)/(2)) then its nine point circle centre is

What is the locus of centres of circles which touch a given line at a given point ?

Locus of the point of intersection of the tangents to the circle x^(2)+y^(2)=a^(2), at the points whose parameters differ by alpha, is

The centres of a set of circles,each of radius 6 ,lie on the circle x^(2)+y^(2)=100 .The locus of any point in the set is

The centres of a set of circles,each of radius 3, lie on the circle x^(2)+y^(2)+25. The locus of any point in the set is:

Locus of middle point of intercept of any tangent with respect to the circle x^(2) + y^(2) =4 between the axis is

Locus of the point of intersection of perpendicular tangents to the circle x^(2)+y^(2)=16 is