If the centroid of an equilateral triangle is (1,1) and its one vertex is (-1, 2), then the equation of its circumcircle is: is `x^2+y^2-2x-2y-3=0` b. `x^2+y^2+2x-2y-3=0` c. `x^2+y^2+2x+2y-3=0` d. none of these

Find the equation of the circle which cuts the circles x^2+y^2+4x+2y+1=0, 2(x^2+y^2)+8x+6y-3=0 and x^2+y^2+6x-2y-3=0 orthogonally.

The equation of the circle passing through the point (1,1) and having two diameters along the pair of lines x^2-y^2-2x+4y-3=0 is a. x^2+y^2-2x-4y+4=0 b. x^2+y^2+2x+4y-4=0 c. x^2+y^2-2x+4y+4=0 d. none of these

Three sides of a triangle are represented by lines whose combined equation is (2x+y-4) (xy-4x-2y+8) = 0 , then the equation of its circumcircle will be : (A) x^2 + y^2 - 2x - 4y = 0 (B) x^2 + y^2 + 2x + 4y = 0 (C) x^2 + y^2 - 2x + 4y = 0 (D) x^2 + y^2 + 2x - 4y = 0

In triangle A B C , the equation of side B C is x-y=0. The circumcenter and orthocentre of triangle are (2, 3) and (5, 8), respectively. The equation of the circumcirle of the triangle is a) x^2+y^2-4x+6y-27=0 b) x^2+y^2-4x-6y-27=0 c) x^2+y^2+4x-6y-27=0 d) x^2+y^2+4x+6y-27=0

The sides of an equilateral triangles are given by x+ 3y , 3x+ 2y - 2 and 4x + (1)/(2) y+ 1

The equation of the circumcircle of an equilateral triangle is x^2+y^2+2gx+2fy+c=0 and one vertex of the triangle in (1, 1). The equation of the incircle of the triangle is a. 4(x^2+y^2)=g^2+f^2 b. 4(x^2+y^2)+8gx+8fy=(1-g)(1+3g)+(1-f)(1+3f) c. 4(x^2+y^2)+8gx+8fy=g^2+f^2 d. None of These

The equation of the incircle of equilateral triangle A B C where B-=(2,0),C-=(4,0), and A lies in the fourth quadrant is: (a) x^2+y^2-6x+(2y)/(sqrt(3))+9=0 (b) x^2+y^2-6x-(2y)/(sqrt(3))+9=0 (c) x^2+y^2+6x+(2y)/(sqrt(3))+9=0 (d) none of these

The equation of the circle which cuts orthogonally the three circles x^2+y^2+4x+2y+1=0, 2x^2+2y^2+8x+6y-3=0, x^2+y^2+6x-2y-3=0 is

The equation of the parabola whose vertex is (a ,0) and the directrix has the equation x+y=3a is a. x^2+y^2+2x y+6a x+10 a y+7a^2=0 b. x^2-2x y+y^2-6a x+10 a y+7a^2=0 c. x^2-2x y+y^2+6a x+10 a y+7a^2=0 d.None of these

For the circles 3x^2+3y^2+x+2y-1=0 , 2x^2+2y^2+2x-y-1=0 radical axis is