If `alpha` is the angle subtended at `P(x_(1),y_(1))` by the circle `S-=x^(2)+y^(2)+2gx+2fy+c=0` then

If theta is the angle subtended by the circle S -= x ^(2) + y ^(2) + 2 gx +2fy+ c =0 at a point P (x _(1) , y _(1)) outside the circle and S_(1) -= x _(1) ^(2) + y _(1) ^(2) + 2 gx _(1) + 2f y _(1) + c, then cos theta is equal too

The equation of the normal at P(x_(1),y_(1)) to the circle x^(2)+y^(2)+2gx+2fy+c=0 is

If PQ, PR are tangents from a point P(x_(1),y_(1)) to the circle x^(2)+y^(2)+2gx+2fy+c=0 show that the circumcircle of the triangle PQR is (x-x_(1))(x+g)+(y-y_(1))(y+f)=0

If PQ, PR are tangents from a point P(x_(1),y_(1)) to the circle x^(2)+y^(2)+2gx+2fy+c=0 show that the circumcircle of the triangle PQR is (x-x_(1))(x+g)+(y-y_(1))(y+f)=0

If the circle x ^(2) + y^(2) + 2gx + 2fy+ c=0 touches X-axis, then

If the circle x ^(2) + y^(2) + 2gx + 2fy+ c=0 touches X-axis, then

If the origin lies inside the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 , then

Statement 1: The least and greatest distances of the point P(10,7) from the circle x^(2)+y^(2)-4x-2y-20=0 are 6 units and 15 units,respectively.Statement 2: A point (x_(1),y_(1)) lies outside the circle S=x^(2)+y^(2)+2gx+2fy+c=0 if S_(1)>0 where S_(1)=x_(1)^(2)+y_(1)^(2)+2gx_(1)+2fy_(1)+c

If p(x_(1) y_(1)) is the midpoint of a chord AB( other than the diameter)of the circle s-=x^(2)+y^(2)+2gx+2fy+c=0 then equation of secant bar(AB) is

The length of the tangent drawn from any point on the circle x^(2) + y^(2) + 2gx + 2fy + a =0 to the circle x^(2) + y^(2) + 2gx + 2fy + b = 0 is