Variable circles are drawn touching two fixed circles externally then locus of centre of variable circle is

Two perpendicular normals to a variable circle are tangent to fixed circle C_(1), with radius 2 units and locus of centre of variable circle be curve C_(2), then find the product of maximum and minimum distances between curves C_(1) and C_(2).

From a point on the circle x^2+y^2=a^2 , two tangents are drawn to the circle x^2+y^2=b^2(a > b) . If the chord of contact touches a variable circle passing through origin, show that the locus of the center of the variable circle is always a parabola.

From a point on the circle x^2+y^2=a^2 , two tangents are drawn to the circle x^2+y^2=b^2(a > b) . If the chord of contact touches a variable circle passing through origin, show that the locus of the center of the variable circle is always a parabola.

From a point on the circle x^2+y^2=a^2 , two tangents are drawn to the circle x^2+y^2=b^2(a > b) . If the chord of contact touches a variable circle passing through origin, show that the locus of the center of the variable circle is always a parabola.

apie circles are drawn touching the line x+5=0 and the circle x^(2)+y^(2)=4 externally.Show that locus of centre of this circle is a partrix and the focus,axis, vertex,directrix and extremities of latus rectum of this parabola.

A circle touches the line L and the circle C_(1) externally such that both the circles are on the same side of the line, then the locus of centre of the circle is :

A circle touches the line L and the circle C_(1) externally such that both the circles are on the same side of the line, then the locus of centre of the circle is :

A variable circle passes through the fixed point (0,5) and touches x -axis.Then l licus of centre of circle (i) parabola (ii)circle (iii)elipse (iv) hyperbola