If a circle with center (-1, 1) touches the line x + 2y + 4 = 0 , then the co-ordinates of the point of contact are

Step-by-step solution

The point of contact is the foot of the perpendicular drawn from the center of the circle to the tangent line. The coordinates of the foot of the perpendicular (h, k) from a point (x₁, y₁) to the line ax + by + c = 0 are given by: h - x₁ a = k - y₁ b = - ax₁ + by₁ + c a^2 + b^2 Substituting (x₁, y₁) = (-1, 1) and the line equation x + 2y + 4 = 0 : h - (-1) 1 = k - 1 2 = - 1(-1) + 2(1) + 4 1^2 + 2^2 h + 1 1 = k - 1 2 = - 5 5 = -1 h + 1 = -1 h = -2 k - 1 2 = -1 k - 1 = -2 k = -1 The coordinates of the point of contac