From any point P tangents of length `t_(1)` and `t_(2)` are drawn to two circles with centre `A,B` and if `PN` is the perpendicular from `P` to the radical axis and `t_(1)^(2)`-`t_(2)^(2)`=`K.PN*AB` then `K=`

If from any point P, tangents PT, PT' are drawn to two given circles with centres A and B respectively, and if PN is the perpendicular from P on their radical axis, then PT^(2) – PT'^(2) =

The tangent at P meets the axes in T and t and CY is the perpendicular on it from the centre; prove that (1)Tt*PY=a^(2)-b^(2)

Two tangents TP and TQ are drawn to a circle with centre O from an external point T . Prove that /_PTQ=2/_OPQ .

In the given figure, from an external point P, a tangent PT and a line segment PAB is drawn to a circle with centre O. ON is perpendicular on the chord AB. Prove that (i)PA.PB=PN^2-AN^2 (ii) PN^2-AN^2 =OP^2-OT^2

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 tangent at P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 cuts the major axis in T and PN is the perpendicular to the x -axis, C being centre then CN.CT

If the tangents at t_(1) and t_(2) to a parabola y^2=4ax are perpendicular then (t_(1)+t_(2))^(2)-(t_(1)-t_(2))^(2) =