Pair of tangents from a point
Two-dimensional geometry · Mathematics
Study notes
Q: Find the pair of tangents from (7,1) to x² + y² = 25. S = x²+y²−25, S₁ = 49+1−25 = 25, T = 7x+y−25. SS₁ = T²: 25(x²+y²−25) = (7x+y−25)². Expand: 25x²+25y²−625 = 49x²+y²+625+14xy−350x−50y. 0 = 24x²−24y²+14xy−350x−50y+1250. (Pair of tangents.)