Find the locus of the centers of the circles `x^2+y^2-2ax-2b y+2=0` , where `a` and `b` are parameters, if the tangents from the origin to each of the circles are orthogonal.

Find the locus of the midpoint of the chord of the circle x^2+y^2-2x-2y=0 , which makes an angle of 120^0 at the center.

Find the locus of the midpoint of the chords of the circle x^2+y^2-ax-by=0 which subtend a right angle at the point (a/2 ,b/2)dot is

Find the differential equation of the family of circles x^(2) + y^(2) = 2ax , where a is a parameter .

Find the locus of the mid points of the chords of the circle x^2 + y^2 -2x -6y - 10 = 0 which pass through the origin.

Find the angle between the two tangents from the origin to the circle (x-7)^2+(y+1)^2=25

Find the differential equation of the family of circles x^(2) + y^(2) = 2ay , where a is a parameter .

The length of the tangent of the circle x^2+y^2-2x-y -7 = 0 from the point (-1,-3) is

Find the locus of the center of the circle touching the circle x^2+y^2-4y-2x=4 internally and tangents on which from (1, 2) are making of 60^0 with each other.

The coordinates of the centre of the circle 2x^(2)+2y^(2) + ax + by + c= 0 are (3, - 4), find a and b.

The equation of the locus of the middle point of a chord of the circle x^2+y^2=2(x+y) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is (a) x+y=2 (b) x-y=2 (c) 2x-y=1 (d) none of these