The locus of the mid-point of a chord of the circle `x^2 + y^2 -2x - 2y - 23=0`, of length 8 units is : (A) `x^2 + y^2 - x - y + 1 =0` (B) `x^2 + y^2 - 2x - 2y - 7 = 0` (C) `x^2 + y^2 - 2x - 2y + 1 = 0` (D) `x^2 + y^2 + 2x + 2y + 5 = 0`

The locus of mid point of chord of the circle x^(2)+y^(2)+2ax-2y-23=0 length 8 unit is

The midpoint of the chord y=x-1 of the circle x^(2)+y^(2)-2x+2y-2=0 is

The locus of mid-points of the chords of the circle x^(2)-2x+y^(2)-2y+1=0 which are of unit length is :

If the middle point of a chord of circle x^(2)+y^(2)+x-y-1=0be(1,1), then length of the chord is:

The equation of the circle passing through (1, 0) and (0, 1) and having smallest possible radius is : (A) 2x^2 + y^2 - 2x-y=0 (B) x^2 + 2y^2 - x - 2y = 0 (C) x^2 = y^2 - x - y = 0 (D) x^2 + y^2 + x + y = 0

y-1=m_1(x-3) and y - 3 = m_2(x - 1) are two family of straight lines, at right angled to each other. The locus of their point of intersection is: (A) x^2 + y^2 - 2x - 6y + 10 = 0 (B) x^2 + y^2 - 4x - 4y +6 = 0 (C) x^2 + y^2 - 2x - 6y + 6 = 0 (D) x^2 + y^2 - 4x - by - 6 = 0

Tangents OA and OB are drawn from the origin to the circle (x-1)^2 + (y-1)^2 = 1 . Then the equation of the circumcircle of the triangle OAB is : (A) x^2 + y^2 + 2x + 2y = 0 (B) x^2 + y^2 + x + y = 0 (C) x^2 + y^2 - x - y = 0 (D) x^2+ y^2 - 2x - 2y = 0

Two circles x^(2) + y^(2) - 2x - 4y = 0 and x^(2) + y^(2) - 8y - 4 = 0