Two circles `S_1` with centre `C_1` and `S_2` with centre `C_2` pass through (a, a) & (2a, 2a) and touches y-axis. Then which of the following is/are true? (Given `C_1(alpha,beta)&C_2(gamma,delta))`

A circle passes through A(2,1) and touches y -axis then the locus of its centre is

A circle passes through A(2,1) and touches y -axis then the locus of its centre is

A circle passes through (0,0) and (1, 0) and touches the circle x^2 + y^2 = 9 then the centre of circle is -

A circle passes through (0,0) and (1, 0) and touches the circle x^2 + y^2 = 9 then the centre of circle is -

A circle passes through (0,0) and (1,0) and touches the circle x^(2)+y^(2)=9 then the centre of circle is -

Two circles each of radius 5 units touch each other at the point (1, 2). If the equation of their common tangent is 4x+3y=10 , and C_(1)(alpha, beta) and C_(2)(gamma, delta), C_(1) ne C_(2) are their centres, then |(alpha+beta) (gamma+delta)| is equal to _______.

Consider circles C_1 & C_2 touching both the axes and passing through (4,4) , then the product of radii of these circles is

The circle S_1 with centre C_1 (a_1, b_1) and radius r_1 touches externally the circle S_2 with centre C_2 (a_2, b_2) and radius r_2 If the tangent at their common point passes through the origin, then

Let the line L : sqrt(2)x y =alpha pass through the point of the intersection P (in the first quadrant) of the circle x^2 y^2 = 3 and the parabola x^2 = 2y . Let the line L touch two circles C_1 and C_2 of equal radius 2 sqrt 3 . If the centres Q_1 and Q_2 of the circles C_1 and C_2 lie on the y-axis, then the square of the area of the triangle PQ_1Q_2 is equal to ___________.