The orthogonal trajectories of the circle `x^(2)+y^(2)-ay=0`, (where a is a parameter), is

The orthogonal trajectories of the family of curves y=Cx^(2) , (C is an arbitrary constant), is

The differential equation representing all possible curves that cut each member of the family of circles x^(2)+y^(2)-2Cx=0 (C is a parameter) at right angle, is

Find the area enclosed by the circle x^(2) + y^(2) = a^(2) .

Obtain equation of circle in x^(2) + y^(2) - x + y = 0

Find the centre and the radius of the circle x^(2)+y^(2)+8x+10y-8=0 .

The value of k such that the family of parabolas y=cx^(2)+k is the orthogonal trajectory of the family of ellipse x^(2)+2y^(2)-y=c, is

Prove that the centres of the circle x^(2) + y^(2) - 4x - 2y + 4 = 0, x^(2) + y^(2) - 2x - 4y + 1 = 0 and x^(2) + y^(2) + 2x - 8y + 1 = 0 are collinear. More over prove that their radii are in geometric pregression.

Smaller area enclosed by the circle x^(2) + y^(2) = 4 and the line x + y = 2 is

The equation to the orthogonal trajectories of the system of parabolas y=ax^2 is