The equation of the pair of tangents at (0,1) to the circle x²+y²-2 x-6 y+6=0 is

Step-by-step solution

Let S x²+y²-2 x-6 y+6=0 and aligned P (x₁, y₁ )=(0,1) S₁=& x₁²+y₁²-2 x₁-6 y₁+6=0 =&(0)²+(1)²-2(0)-6(1)+6 =& 1-6+6=1 T=& x x₁+y y₁- (x+x₁ )-3 (y+y₁ )+6 =& x (0)+y(1)-(x+0)-3(y+1)+6 =& 0+y-x-3 y-3+6 =&-x-2 y+3 aligned aligned T² &=(-x-2 y+3)² &=(-x-2 y)²+9+6(-x-2 y) &=x²+4 y²+4 x y+9-6 x-12 y aligned Equation of the pair of tangents S S₁=T² (x²+y²-2 x-6 y+6 )(1) =x²+4 y²+4 x y-6 x-12 y+9 3 y²+4 x y-4 x-6 y+3=0