From a point on the circle `x^2+y^2=a^2` , two tangents are drawn to the circle `x^2+y^2=b^2(a > b)` . If the chord of contact touches a variable circle passing through origin, show that the locus of the center of the variable circle is always a parabola.

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:

From a point P tangents are drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 If the chord of contact touches the auxiliary circle then the locus of P is

A variable circle passes through the fixed point (2,0) and touches y-axis then the locus of its centre is

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 B and C. Find the locus of the circumcenter of hat varphi ABC.

From every point on the line x+y=4 ,tangents are drawn to circle x^(2)+y^(2)=4 .Then,all chord of contact passes through (x_(1),y_(1)),x_(1)+y_(1)=

A variable circle passes through the fixed point (2, 0) and touches y-axis Then, the locus of its centre, is

Let the midpoint of the chord of contact of tangents drawn from A to the circle x^(2) + y^(2) = 4 be M(1, -1) and the points of contact be B and C

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