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

The equation of the normal at (1,2) to the circle x^(2)-y^(2)-4x-6y-12=0 is

Equation of normal at P(3,-4) to the circle x^(2)+y^(2)-10x-2y+6=0 is

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

The equation of the diameter of the circle x^(2)+y^(2)+2gx+2fy+c=0 which corresponds to the chord ax+by+d=0 is lambda x-ay+mu g+k=0 then lambda+mu is

The equation to the normal to the circle x^(2)+y^(2)-2x-2y-2=0 at the point (3,1) on it is

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

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

The centre of the circle that cuts the circle x^(2)+y^(2)+2gx+2fy+c=0 and lines x=g and y=f orthogonally is

What is the length of the intercept made on the x-axis by the circle x^(2) +y^(2) + 2gx + 2fy + c = 0 ?