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

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

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 L_(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. Equation of C_(1) 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=

If x^(2)+y^(2)=t+t^(-1),x^(4)+y^(4)=t^(2)+t^(-2)," then " yy_(1)=

A unit tangent vector at t=2 on the curve x=t^(2)+2, y=4t-5 and z=2t^(2)-6t is

The radius of the circle t^(2) x^(2) + t^(2) y^(2) - 2at^(3) x - 2 aty + a^(2) t^(4) - a^(2) t^(2) + a^(2) = 0 is

Find the slope of the tangent to the curve x=t^2+3t-8 , y=2t^2-2t-5 at t=2 .