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).

Answer

4