If points `Aa n dB` are (1, 0) and (0, 1), respectively, and point `C` is on the circle `x^2+y^2=1` , then the locus of the orthocentre of triangle `A B C` is `x^2+y^2=4` `x^2+y^2-x-y=0` `x^2+y^2-2x-2y+1=0` `x^2+y^2+2x-2y+1=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

The coordinates of the orthocentre of the triangle formedby the lines 2x^(2)-3xy+y^(2)=0 and x+y=1 are

If y=c is a tangent to the circle x^(2)+y^(2)–2x+2y–2 =0 at (1, 1), then the value of c is

At what points on the curve x^(2)+y^(2)-2x-4y+1=0, the tangents are parallel to the y-a is?

The point (1,2) lies inside the circle x^(2)+y^(2)-2x+6y+1=0 .

From the points (3,4), chords are drawn to the circle x^(2)+y^(2)-4x=0 .The locus of the midpoints of the chords is (a) x^(2)+y^(2)-5x-4y+6=0(b)x^(2)+y^(2)+5x-4y+6=0(c)x^(2)+y^(2)-5x+4y+6=0(d)x^(2)+y^(2)-5x-4y-6=0

Discuss the position of the points (1,2) and (6,0) with respect to the circle x^2+y^2-4x+2y-11=0

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 tangents to the circle x^(2)+y^(2)-4x+2y+k=0 at (1,1) is x-2y+1=0 then k=