From the variable point `A` on circle `x^2+y^2=2a^2,` two tangents are drawn to the circle `x^2+y^2=a^2` which meet the curve at `Ba n dCdot` Find the locus of the circumcenter of ` A B Cdot`

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at Aa n dB . Then find the locus of the midpoint of A Bdot

From an arbitrary point P on the circle x^2+y^2=9 , tangents are drawn to the circle x^2+y^2=1 , which meet x^2+y^2=9 at Aa n dB . The locus of the point of intersection of tangents at Aa n dB to the circle x^2+y^2=9 is x^2+y^2=((27)/7)^2 (b) x^2-y^2((27)/7)^2 y^2-x^2=((27)/7)^2 (d) none of these

From points on the circle x^2+y^2=a^2 tangents are drawn to the hyperbola x^2-y^2=a^2 . Then, the locus of mid-points of the chord of contact of tangents is:

If from any point on the circle x^(2)+y^(2)=a^(2) tangents are drawn to the circle x^(2)+y^(2)=b^(2), (a>b) then the angle between tangents is

The locus of the point of intersection of the two tangents drawn to the circle x^(2)+y^(2)=a^(2) which include are angle alpha is

From the points on the circle x^(2)+y^(2)=a^(2) , tangents are drawn to the hyperbola x^(2)-y^(2)=a^(2) : prove that the locus of the middle-points (x^(2)-y^(2))^(2)=a^(2)(x^(2)+y^(2))

Two perpendicular tangents to the circle x^(2)+y^(2)=a^(2) meet at P. Then the locus of P has the equation

Two perpendicular tangents to the circle x^(2) + y^(2) = a^(2) meet at P. Then the locus of P has the equation

Tangents are drawn from (4, 4) to the circle x^(2) + y^(2) – 2x – 2y – 7 = 0 to meet the circle at A and B. The length of the chord AB is