Find the equation of the two tangents from the point `(0, 1 )` to the circle `x^2 + y^2-2x + 4y = 0`

Find the equations of the tangents from the point A(3,2) to the circle x^(2)+y^(2)+4x+6y+8=0 .

Find the equation of the tangent and normal at (1, 1) to the circle 2x^(2) + 2 y^(2) - 2x - 5y + 3 = 0

The angle between the pair of tangents from the point (1, 1/2) to the circle x^2 + y^2 + 4x + 2y -4 = 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).

Find the angle between the tangents drawn from (3, 2) to the circle x^(2) + y^(2) - 6x + 4y - 2 = 0

Find the equation of pair of tangents from (i) (0,0) to the circle x^(2)+y^(2)+10x+10y+40=0 (ii) (4,10) to the circle x^(2)+y^(2)=25 (iii) (3,2) to the circle x^(2)+y^(2)-6x+4y-2=0 (iv) (10,4) to the circle x^(2)+y^(2)=25 (v) (1,3) to the circle x^(2)+y^(2)-2x+4y-11=0

Find the equation of tangent and normal at (3, 2) of the circle x^(2) + y^(2) - 3y - 4 = 0.

Find the equation to the chord of contact of the tangents drawn from an external point (-3, 2) to the circle x^2 + y^2 + 2x-3=0 .

Find the equation to the chord of contact of the tangents drawn from an external point (-3, 2) to the circle x^2 + y^2 + 2x-3=0 .

Find the angle between the pair of tangents drawn from (1, 3) to the circle x^(2) + y^(2) - 2 x + 4y - 11 = 0