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

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

Length of the tangent. Prove that the length t o f the tangent from the point P (x_(1), y(1)) to the circle x^(2) div y^(2) div 2gx div 2fy div c = 0 is given by t=sqrt(x_(1)^(2)+y_(1)^(2)+2gx_(1)+2fy_(1)+c) Hence, find the length of the tangent (i) to the circle x^(2) + y^(2) -2x-3y-1 = 0 from the origin, (2,5) (ii) to the circle x^(2)+y^(2)-6x+18y+4=-0 from the origin (iii) to the circle 3x^(2) + 3y^(2)- 7x - 6y = 12 from the point (6, -7) (iv) to the circle x^(2) + y^(2) - 4 y - 5 = 0 from the point (4, 5).

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

The equation of the tangents drawn from the origin to the circle x^(2)+y^(2)-2gx-2fy+f^(2)=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

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