From the origin O tangents OP and OQ are drawn to the circle `x^(2) + y^(2) + 2gx + 2fy + c = 0`. Then the circumcentre of the triangle OPQ lies at

If O is the origin and OP, OQ are distinct tangents to the circle x^(2)+y^(2)+2gx+2fy+c=0 then the circumcentre of the triangle OPQ is

Tangents OP and OQ are drawn from the origin o to the circle x^2 + y^2 + 2gx + 2fy+c=0. Find the equation of the circumcircle of the triangle OPQ .

STATEMENT -1 : if O is the origin and OP and OQ are tangents to the circle x^(2) + y^(2) + 2x + 4y + 1 = 0 the circumcentre of the triangle is ((-1)/(2), -1) . and STATEMENT-2 : OP.OQ = PQ^(2) .

The circle x^(2) + y^(2) + 2g x + 2fy + c = 0 does not intersect the y-axis if

Find the centre and radius of the circle ax^(2) + ay^(2) + 2gx + 2fy + c = 0 where a ne 0 .

From a point P perpendicular tangents PQ and PR are drawn to ellipse x^(2)+4y^(2) =4 , then locus of circumcentre of triangle PQR is

Two tangents OA and OB are drawn to the circle x^(2)+y^(2)+4x+6y+12=0 from origin O. The circumradius of DeltaOAB is :

Find the pair of tangents from the origin to the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 and hence deduce a condition for these tangents to be perpendicular.

If O is the origin and O Pa n dO Q are the tangents from the origin to the circle x^2+y^2-6x+4y+8-0 , then the circumcenter of triangle O P Q is (3,-2) (b) (3/2,-1) (3/4,-1/2) (d) (-3/2,1)

From a point R(5, 8) two tangents RP and RQ are drawn to a given circle s=0 whose radius is 5. If circumcentre of the triangle PQR is (2, 3), then the equation of circle S = 0 is