Let the latus ractum of the parabola `y^(2) = 4x` be the comon chord to the circles `C_(1)` and `C_(2)` each of them having radius `2 sqrt(5)` . Then , the distance the centre of the circles `C_(1)` and `C_(2)` is :

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 ___________.

Let PQ be the focal chord of the parabola y^(2)=4x . If the centre of the circle having PQ as its diameter lies on the line y=(4)/(sqrt5) , then the radius (in units) is equal to

Let C_(1) be the circle of radius r > 0 with centre at (0,0) and let C_(2) be the circle of radius r with centre at (r,0) .The length of the arc of the circle C_(1) that lies inside the circle C_(2) ,is

Let PQ be a focal chord of the parabola y^(2)=4x . If the centre of a circle having PQ as its diameter lies on the line sqrt5y+4=0 , then length of the chord PQ , is

Let PQ be a focal chord of the parabola y^(2)=4x . If the centre of a circle having PQ as its diameter lies on the line sqrt5y+4=0 , then length of the chord PQ, is

If a diameter of the circle x^(2) + y^(2) - 2x - 6y + 6 = 0 is a chord of another circle C having centre (2, 1), then the radius of the circle C is