`t_(1),t_(2),t_(3)` are lengths of tangents drawn from a point (h,k) to the circles `x^(2)+y^(2)=4,x^(2)+y^(2)-4=0andx^(2)+y^(2)-4y=0` respectively further, `t_(1)^(4)=t_(2)^(2)" "t_(3)^(2)+16`. Locus of the point (h,k) consist of a straight line `L_(1)` and a circle `C_(1)` passing through origin. A circle `C_(2)` , which is equal to circle `C_(1)` is drawn touching the line `L_(1)` and the circle `C_(1)` externally.
Equation of `C_(1)` is

t_(1),t_(2),t_(3) are lengths of tangents drawn from a point (h,k) to the circles x^(2)+y^(2)=4,x^(2)+y^(2)-4=0andx^(2)+y^(2)-4y=0 respectively further, t_(1)^(4)=t_(2)^(2)" "t_(3)^(2)+16 . Locus of the point (h,k) consist of a straight line L_(1) and a circle C_(1) passing through origin. A circle C_(2) , which is equal to circle C_(1) is drawn touching the line L_(1) and the circle C_(1) externally. The distance between the centres of C_(1)andC_(2) is

Let t_(1),t_(2),t_(3) be the lengths of tangents from a point P to the circles x^(2)+y^(2)=a^(2) ,x^(2)+y^(2)=2ax, x^(2)+y^(2)=2ay respectively .If t_(1)^(4)=t_(2)^(2)t_(3)^(2)+a^(4) ., then the locus of P is

The length of the transversal common tangent to the circle x^(2)+y^(2)=1 and (x-t)^(2)+y^(2)=1 is sqrt(21) , then t=

Number of tangents that can be drawn from the point (4 sqrt(t), 3(t-1)) to the ellipse (x^(2))/(16)+(y^(2))/(9)=1

If t_(1) and t_(2) are the lengths of tangents drawn on circle with radius r from two conjugate points A,B then t_(1)^(2)+t_(2)^(2)=

The chord of contact of (2,1) w.r.t to the circle x^(2)+y^(2)+4x+4y+1=0 is