The chord of contact of a point `A(x_(A), y_(A))` of `y^(2)=4x` passes through (3, 1) and point A lies on `x^(2)+y^(2)=5^(2)`. Then :

If the chord of contact of tangents from a point (x_(1),y_(1)) to the circle x^(2)+y^(2)=a^(2) touches the circle (x-a)^(2)+y^(2)=a^(2), then the locus of (x_(1),y_(1)) is

If the chord of contact of tangents from a point (x_1, y_1) to the circle x^2 + y^2 = a^2 touches the circle (x-a)^2 + y^2 = a^2 , then the locus of (x_1, y_1) is

If the chord of contact of tangents from a point P (x_1,y_1) to the circle x^2+y^2=a^2 touches the circle (x-a)^2+y^2 = a^2 , then the locus of (x_1, y_1) is :

If the chord of contact of tangents from a point (x_1,y_1) to the circle x^2+y^2=a^2 touches the circle (x-a)^2+y^2=a^2 , then the locus of (x_1,y_1) is :

The chords of contact of the pair of tangents drawn from each point on the line 2x + y =4 to the circle x^(2) +y^(2) =1 pass through the point "___________" .

The chords of contact of the pair of tangents drawn from each point on the line 2x + y =4 to the circle x^(2) +y^(2) =1 pass through the point "___________" .

The point of contact of 5x+6y+1=0 to the hyperbola 2x^(2)-3y^(2)=2 is

The point of contact of 5x+6y+1=0 to the hyperbola 2x^(2)-3y^(2)=2 is