A chord AB of circle `x^(2) +y^(2) =a^(2)` touches the circle `x^(2) +y^(2) - 2ax =0`.Locus of the point of intersection of tangens at A and B is `:`

There are two perpendicular lines, one touches to the circle x^(2) + y^(2) = r_(1)^(2) and other touches to the circle x^(2) + y^(2) = r_(2)^(2) if the locus of the point of intersection of these tangents is x^(2) + y^(2) = 9 , then the value of r_(1)^(2) + r_(2)^(2) is.

Two variable chords AB and BC of a circle x^(2)+y^(2)=a^(2) are such that AB=BC=a ,then locus of point of intersection of tangents at A and C is a circle of radius lambda a , where lambda is

The tangents PA and PB are drawn from any point P of the circle x^(2)+y^(2)=2a^(2) to the circle x^(2)+y^(2)=a^(2) . The chord of contact AB on extending meets again the first circle at the points A' and B'. The locus of the point of intersection of tangents at A' and B' may be given as

The tangents PA and PB are drawn from any point P of the circle x^(2)+y^(2)=2a^(2) to the circle x^(2)+y^(2)=a^(2) . The chord of contact AB on extending meets again the first circle at the points A' and B'. The locus of the point of intersection of tangents at A' and B' may be given as

The equation of the locus of the middle point of a chord of the circle x^(2)+y^(2)=2(x+y) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is x+y=2( b) x-y=22x-y=1( d ) none of these

If the polar of a point P w.r.t the circle x^(2)+y^(2)=a^(2) touches the parabola y^(2)=4ax then the locus of P is